Melvin Henriksen died October 14, 2009, at the age of 82.
You might be interested in reading his obituary, or about the conference the department held to celebrate his life and his work.
Education
- Ph.D. Mathematics, University of Wisconsin, 1951
- M.S. Mathematics, University of Wisconsin, 1949
- B.S. Mathematics, City College of New York, 1948
Professional History
- 1997–present Professor Emeritus, Department of Mathematics, Harvey Mudd College
- 1969–1997 Professor of Mathematics, Harvey Mudd College
- 1993–1994 Visiting Professor, Department of Mathematics, Wesleyan University
- 1983 Visiting Professor, Department of Mathematics, Wesleyan University
- 1978–1979 Visiting Professor, Department of Mathematics, Wesleyan University
- 1975–1976 Research Associate at the University of Manitoba
- 1969–1972 Chair, Department of Mathematics, Harvey Mudd College
- 1986–1987 Visiting Professor at Wesleyan University
- 1968–1969 Research Associate, Department of Mathematics, UC Berkeley
- 1965–1968 Head, Department of Mathematics, Case Western
- 1961–1965 Professor of Mathematics, Purdue University
- 1960–1961 Professor of Mathematics, Wayne State University
- 1957–1961 Associate Professor of Mathematics, Purdue University
- 1953–1957 Assistant Professor of Mathematics, Purdue University
- 1952–1953 Instructor of Mathematics, Purdue University
- 1951–1952 Assistant Professor of Mathematics, University of Alabama
- 1950–1951 Instructor of Mathematics, University of Wisconsin, Extension
- 1948–1950 Teaching Assistant, Dept. of Mathematics, University of Wisconsin
Specialties
- Ordered Algebraic Systems & General Topology
Ph.D. Dissertations Directed
- Seven at Purdue University
- One at Case Western Reserve University
- Three at Claremont Graduate School
Professional Societies
- American Mathematical Society
- Mathematical Association of America
- National Association of Mathematicians
Service to Professional Societies
- Member of the Membership Committee, American Mathematical Society, 1984–1990
- Program Chair, Southern California Section of the Mathematical Association of America, 1984–1986
- Member of the Executive Committee of the Southern California Section of the Mathematical Association of America, 1990–1994 and Section Chair, 1992–1993
- Member of the Organizing Committee for the Summer Topology Conference, 1990–1995 and 1999–present
- Associate Editor, American Mathematical Monthly, 1988–1991
- Associate Editor, Algebra Universalis, 1993–present
Biographical Listings
See biographies in Who's Who in America and American Men of Science.
Publications
Books
- Single Variable Calculus with an Introduction to Numerical Methods, with M. Lees, Worth Publishing Co., New York, 1970.
Film
- Infinite Acres, Mathematical Association of America, 1965.
Reviewed Publications
- Azadi, H.; Henriksen, Melvin; Momtahan, Ehsan. Some properties of algebras of real-valued measurable functions. Acta Math. Hungar.. 124 (2009), no. 1, 15–23. (PDF)
- Henriksen, Melvin; Raphael, R.; Woods, R. G.. SP-scattered spaces; a new generalization of scattered spaces Comment. Math. Univ. Carolin. 48 (2007), no. 3, 487–505. (PDF)
- Bikram Banerjee; Henriksen, Melvin. Ways in which C(X) mod a prime ideal can be a valuation domain: something old and something new. Positivity, Trends in Mathematics, Birkhauser Verlag (2007), 1–25. (PDF)
- Henriksen, Melvin; Amir Nikou. Removing sets from connected spaces while preserving connectedness. Comment. Math. Univ. Carolin. 48 (2007), no. 1, 119–134. (PDF)
- Osba, Emad Abu; Henriksen, Melvin; Alkam, Osama; Smith, F. A. The maximal regular ideal of some commutative rings. Comment. Math. Univ. Carolin. 47 (2006), no. 1, 1–10. (PDF)
- Golasiński, Marek; Henriksen, Melvin Residue class rings of real-analytic and entire functions. Colloq. Math. 104 (2006), 85–97. (PDF)
- Henriksen, Melvin Summary of results on the maximal regular ideal of some commutative rings. Proceedings of 6th International Pure Mathematics Conference 2005. 44–49.
- Henriksen, Melvin; Biswajit Mitra. C(X) can sometimes determine X without X being realcompact. Comment. Math. Univ. Carolin. 46 (2005), no. 4, 711–720. (PDF)
- Henriksen, Melvin; Janos, L; and Woods, R.G. Properties of one-point completions of a noncompact metrizable space. Comment. Math. Univ. Carolin. 46 (2005), no. 1, 105–123. (PDF)
- Osba, Emad Abu; Henriksen, Melvin Essential P-spaces: a generalization of door spaces. Comment. Math. Univ. Carolin. 45 (2004), no. 3, 509–518. (PDF)
- Osba, Emad Abu; Henriksen, Melvin; Alkam, Osama Combining local and von Neumann regular rings. Comm. Algebra 32 (2004), no. 7, 2639–2653. (PDF)
- Henriksen, M.; Woods, R. G. Cozero complemented spaces; when the space of minimal prime ideals of a C(X) is compact. Topology Appl. 141 (2004), no. 1-3, 147–170. (PDF)
- Henriksen, Melvin; Martínez, Jorge; Woods, R. Grant Spaces X in which all prime z-ideals of C(X) are minimal or maximal. Comment. Math. Univ. Carolin. 44 (2003), no. 2, 261–294. (PDF)
- Henriksen, Melvin; Walters-Wayland, Joanne A pointfree study of bases for spaces of minimal prime ideals. Quaest. Math. 26 (2003), no. 3, 333–346. (PDF)
- Boulabiar, Karim; Buskes, Gerard; Henriksen, Melvin A generalization of a theorem on biseparating maps. J. Math. Anal. Appl. 280 (2003), no. 2, 334–349. (PDF)
- Henriksen, Melvin Old and new unsolved problems in lattice-ordered rings that need not be f-rings. Ordered algebraic structures, 11–17, Dev. Math., 7, Kluwer Acad. Publ., Dordrecht, 2002. (PDF)
- Henriksen, Melvin Topology related to rings of real-valued continuous functions Recent Progress in General Topology II, eds. M. Husek, J. van Mill, 553–556, Elsevier Science, 2002. (PDF)
- Henriksen, M.; Raphael, R.; Woods, R. G. A minimal regular ring extension of C(X). Fund. Math. 172 (2002), no. 1, 1–17. (PDF)
- Henriksen, Melvin; Kopperman, Ralph; Rayburn, Marlon; Todd, Aaron R. Corrections to: "Oxtoby's pseudocompleteness revisited" [Topology Appl. (2000), no. 2-3, 119–132; MR1733039 (2001a:54005)]. Topology Appl. 114(2001), no. 1, 115–116. (PDF)
- Henriksen, Melvin; Kopperman, Ralph; Rayburn, Marlon; Todd, Aaron R. Oxtoby's pseudocompleteness revisited. Topology Appl. 100 (2000), no. 2-3, 119–132. (PDF)
- Alas, O. T.; Comfort, W. W.; Garcia-Ferreira, S.; Henriksen, M.; Wilson, R. G.; Woods, R. G. When is |C(X\times Y)| = |C(X)||C(Y)|? Houston J. Math. 26 (2000), no. 1, 83–115. (PDF)
- Henriksen, M.; Smith, F. A. A look at biseparating maps from an algebraic point of view. Real algebraic geometry and ordered structures (Baton Rouge, LA, 1996), 135–144, Contemp. Math., 253, Amer. Math. Soc., Providence, RI, 2000. (PDF)
- Henriksen, Melvin; Smith, F. A. The Bordalo order on a commutative ring. Comment. Math. Univ. Carolin. 40 (1999), no. 3, 429–440. (PDF)
- Henriksen, M.; Woods, R. G. Separate versus joint continuity: a tale of four topologies. Special issue in honor of W. W. Comfort (Curacao, 1996). Topology Appl. 97 (1999), no. 1-2, 175–205. (PDF)
- Henriksen, Melvin Rings of continuous functions in the 1950s. Handbook of the history of general topology, Vol. 1, 243–253, Kluwer Acad. Publ., Dordrecht, 1997. (PDF)
- Henriksen, M.; Kopperman, R.; Mack, J.; Somerset, D. W. B. Joincompact spaces, continuous lattices, and C\sp *-algebras. Algebra Universalis 38 (1997), no. 3, 289–323. (PDF)
- Henriksen, Melvin Separate vs. joint continuity. A tale of four topologies–-a summary. Proceedings of the Tennessee Topology Conference (Nashville, TN, 1996), 67–84, World Sci. Publishing, River Edge, NJ, 1997. (PDF)
- Henriksen, Melvin A survey of f-rings and some of their generalizations. Ordered algebraic structures (Curaçao, 1995), 1–26, Kluwer Acad. Publ., Dordrecht, 1997. (PDF)
- Henriksen, Melvin; Larson, Suzanne; Martinez, Jorge The intermediate value theorem for polynomials over lattice-ordered rings of functions. Papers on general topology and applications (Amsterdam, 1994), 108–123, Ann. New York Acad. Sci., 788, New York Acad. Sci., New York, 1996. (PDF)
- Gillman, Leonard; Henriksen, Melvin Meyer Jerison (1922–1995). Notices Amer. Math. Soc. 43 (1996), no. 1, 17–18.
- Henriksen, Melvin; Larson, Suzanne; Martinez, Jorge; Woods, R. G. Lattice-ordered algebras that are subdirect products of valuation domains. Trans. Amer. Math. Soc. 345 (1994), no. 1, 195–221. (PDF)
- Dow, A.; Henriksen, M.; Kopperman, R.; Woods, R. G. Topologies and cotopologies generated by sets of functions. Houston J. Math. 19 (1993), no. 4, 551–586. (PDF)
- Henriksen, Melvin; Larson, Suzanne Semiprime f-rings that are subdirect products of valuation domains. Ordered algebraic structures (Gainesville, FL, 1991), 159–168, Kluwer Acad. Publ., Dordrecht, 1993. (PDF)
- Henriksen, M.; Wilson, R. G. Almost discrete SV-spaces. Topology Appl. 46 (1992), no. 2, 89–97. (PDF)
- Henriksen, Melvin; Wilson, Richard When is C(X)/P a valuation ring for every prime ideal P? Proceedings of the Symposium on General Topology and Applications (Oxford, 1989). Topology Appl. 44 (1992), no. 1-3, 175–180. (PDF)
- Henriksen, M.; Larson, S.; Smith, F. A. When is every order ideal a ring ideal? Comment. Math. Univ. Carolin. 32 (1991), no. 3, 411–416. (PDF)
- Henriksen, Melvin Topologies and cotopologies generated by sets of functions: a preview. General topology and applications (Staten Island, NY, 1989), 115–128, Lecture Notes in Pure and Appl. Math., 134, Dekker, New York, 1991.
- Henriksen, M.; Kopperman, R. A general theory of structure spaces with applications to spaces of prime ideals. Algebra Universalis 28 (1991), no. 3, 349–376. (PDF)
- Henriksen, Melvin Spaces with a pretty base. Proceedings of the Conference on Locales and Topological Groups (Curaçao, 1989). J. Pure Appl. Algebra 70 (1991), no. 1-2, 81–87. (PDF)
- Henriksen, Melvin Spaces of prime ideals. Fourth Conference on Topology (Italian) (Sorrento, 1988). Rend. Circ. Mat. Palermo (2) Suppl. No. 24 (1990), 127–144. (PDF)
- Henriksen, Melvin; Kopperman, Ralph Bitopological spaces of ideals. General topology and applications (Middletown, CT, 1988), 133–141, Lecture Notes in Pure and Appl. Math., 123, Dekker, New York, 1990. (PDF)
- Henriksen, M.; Smith, F. A. Ordered ultraconnected rings. Comment. Math. Univ. Carolin. 31 (1990), no. 1, 41–47. (PDF)
- Henriksen, Melvin. Rings of continuous functions from an algebraic point of view. Ordered algebraic structures (Curaçao, 1988), 143–174, Math. Appl., 55, Kluwer Acad. Publ., Dordrecht, 1989. (PDF)
- Henriksen, Melvin Rings with a unique regular element. Rings, modules and radicals (Hobart, 1987), 78–87, Pitman Res. Notes Math. Ser., 204, Longman Sci. Tech., Harlow, 1989. (PDF)
- Henriksen, Melvin; Woods, R. G. F-spaces and sub-Stonean spaces: general topology as a tool in functional analysis. Papers on general topology and related category theory and topological algebra (New York, 1985/1987), 60–68, Ann. New York Acad. Sci., 552, New York Acad. Sci., New York, 1989. (PDF)
- Henriksen, M.; Vermeer, J.; Woods, R. G. Wallman covers of compact spaces. Dissertationes Math. (Rozprawy Mat.) 280 (1989), 34 pp. (PDF)
- Henriksen, Melvin; Woods, R. G. Weak P-spaces and L-closed spaces. Questions Answers Gen. Topology 6 (1988), no. 2, 201–207. (PDF)
- Dow, A.; Henriksen, M.; Kopperman, Ralph; Vermeer, J. The space of minimal prime ideals of C(X) need not be basically disconnected. Proc. Amer. Math. Soc. 104 (1988), no. 1, 317–320. (PDF)
- Feldman, David; Henriksen, Melvin f-rings, subdirect products of totally ordered rings, and the prime ideal theorem. Nederl. Akad. Wetensch. Indag. Math. 50 (1988), no. 2, 121–126. (PDF)
- Henriksen, M.; Peters, T. J. Locally finite families, completely separated sets and remote points. Proc. Amer. Math. Soc. 103 (1988), no. 3, 989–995. (PDF)
- Henriksen, Melvin; Rayburn, Marlon C. Nearly pseudocompact extensions. Math. Japon. 32 (1987), no. 4, 569–582. (PDF)
- Henriksen, M.; Vermeer, J.; Woods, R. G. Quasi F-covers of Tychonoff spaces. Trans. Amer. Math. Soc. 303 (1987), no. 2, 779–803. (PDF)
- Henriksen, M.; Kopperman, R.; Smith, F. A. Ordered products of topological groups. Math. Proc. Cambridge Philos. Soc. 102 (1987), no. 2, 281–295. (PDF)
- Day, Jane M.; Henriksen, Melvin Iterative solutions of systems of linear equations whose coefficient matrix is positive real. Linear and Multilinear Algebra 19 (1986), no. 3, 267–285. (PDF)
- Henriksen, Melvin E. Unsolved problems on algebraic aspects of C(X). Rings of continuous functions (Cincinnati, Ohio, 1982), 195–202, Lecture Notes in Pure and Appl. Math., 95, Dekker, New York, 1985. (PDF)
- Henriksen, Melvin Gauge functions and the divisor chain condition. Internat. J. Math. Ed. Sci. Tech. 14 (1983), no. 5, 551–553. (PDF)
- Henriksen, M.; Smith, F. A. Sums of z-ideals and semiprime ideals. General topology and its relations to modern analysis and algebra, V (Prague, 1981), 272–278, Sigma Ser. Pure Math., 3, Heldermann, Berlin, 1983. (PDF)
- Henriksen, Melvin; Smith, F. A. Some properties of positive derivations on f-rings. Ordered fields and real algebraic geometry (San Francisco, Calif., 1981), pp. 175–184, Contemp. Math., 8, Amer. Math. Soc., Providence, R.I., 1982. (PDF)
- Henriksen, Melvin; Rayburn, Marlon C. On nearly pseudocompact spaces. Topology Appl. 11 (1980), no. 2, 161–172. (PDF)
- Dashiell, F.; Hager, A.; Henriksen, M. Order-Cauchy completions of rings and vector lattices of continuous functions. Canad. J. Math. 32 (1980), no. 3, 657–685. (PDF)
- Henriksen, M. A summary of results on order-Cauchy completions of rings and vector lattices of continuous functions. Edited by Ross Geoghegan. Topology Proc. 4 (1979), no. 1, 239–263 (1980). (PDF)
- Henriksen, Melvin An algebraic characterization of the Freudenthal compactification for a class of rimcompact spaces. Proceedings of the 1977 Topology Conference (Louisiana State Univ., Baton Rouge, La., 1977), I. Topology Proc. 2 (1977), no. 1, 169–178 (1978). (PDF)
- Henriksen, Melvin Some sufficient conditions for the Jacobson radical of a commutative ring with identity to contain a prime ideal. Portugal. Math. 36 (1977), no. 3-4, 257–269 (1980). (PDF)
- Henriksen, Melvin Semiprime ideals of f-rings. Symposia Mathematica, Vol. XXI (Convegno sulle Misure su Gruppi e su Spazi Vettoriali, Convegno sui Gruppi e Anelli Ordinati, INDAM, Rome, 1975), pp. 401–409. Academic Press, London, 1977. (PDF)
- Henriksen, Melvin Tychonoff spaces that have a compactification with countable remainder. General topology and its relations to modern analysis and algebra, IV (Proc. Fourth Prague Topological Sympos., Prague, 1976), Part B, pp. 164–167. Soc. Czech. Mathematicians and Physicists, Prague, 1977. (PDF)
- Henriksen, Melvin Conditions that guarantee that all nilpotents commute with every element of an alternative ring. Algebra Universalis 7 (1977), no. 1, 119–132. (PDF)
- Henriksen, Melvin Uniformly closed ideals of uniformly closed algebras of extended real-valued functions. Symposia Mathematica, Vol. XVII (Convegno sugli Anelli di Funzioni Continue, INDAM, Roma, 1973), pp. 49–53. Academic Press, London, 1976. (PDF)
- Chinburg, Ted; Henriksen, Melvin Multiplicatively periodic rings. Amer. Math. Monthly 83 (1976), no. 7, 547–549. (PDF)
- Chinburg, Ted; Henriksen, Melvin Sums of k-th powers in the ring of polynomials with integer coefficients. Acta Arith. 29 (1976), no. 3, 227–250. (PDF)
- Henriksen, Melvin A simple characterization of commutative rings without maximal ideals. Amer. Math. Monthly 82 (1975), 502–505. (PDF)
- Chinburg, Ted; Henriksen, Melvin Sums of kth powers in the ring of polynomials with integer coefficients. Bull. Amer. Math. Soc. 81 (1975), 107–110. (PDF)
- Henriksen, Melvin Two classes of rings generated by their units. J. Algebra 31 (1974), 182–193. (PDF)
- Henriksen, Melvin On a class of regular rings that are elementary divisor rings. Arch. Math. (Basel) 24 (1973), 133–141. (PDF)
- Henriksen, M. On difficulties in embedding lattice-ordered integral domains in lattice-ordered fields. General topology and its relations to modern analysis and algebra, III (Proc. Third Prague Topological Sympos., 1971), pp. 183–185. Academia, Prague, 1972. (PDF)
- Henriksen, M.; Jerison, M. The space of minimal prime ideals of a commutative ring. Trans. Amer. Math. Soc. 115 1965 110–130. (PDF)
- Henriksen, M.; Jerison, M. Minimal projective extensions of compact spaces. Duke Math. J. 32 1965 291–295. (PDF)
- Henriksen, Melvin; Isbell, J. R. Averages of continuous functions on countable spaces. Bull. Amer. Math. Soc. 70 1964 287–290. (PDF)
- Henriksen, Melvin; Isbell, J. R. Lattice-ordered rings and function rings. Pacific J. Math. 12 1962 533–565. (PDF)
- Henriksen, M.; Jerison, M. The space of minimal prime ideals of a commutative ring. 1962 General Topology and its Relations to Modern Analysis and Algebra (Proc. Sympos., Prague, 1961) pp. 199–203 Academic Press, New York; Publ. House Czech. Acad. Sci., Prague. (PDF)
- Henriksen, M.; Johnson, D. G. On the structure of a class of archimedean lattice-ordered algebras. Fund. Math. 50 1961/1962 73–94. (PDF)
- Henriksen, M.; Isbell, J. R.; Johnson, D. G. Residue class fields of lattice-ordered algebras. Fund. Math. 50 1961/1962 107–117. (PDF)
- Henriksen, Melvin Multiplicative summability methods and the Stone-\v Cech compactification. Math. Z. 71 1959 427–435. (PDF)
- Henriksen, Melvin The a\sp{n(a)}=a theorem for semirings. Math. Japon 5 1958/1959 21–24. (PDF)
- Henriksen, Melvin; Isbell, J. R. Some properties of compactifications. Duke Math. J. 25 1957 83–105. (PDF)
- Henriksen, Melvin; Isbell, J. R. Local connectedness in the Stone-\v Cech compactification. Illinois J. Math. 1 1957 574–582. (PDF)
- Henriksen, Melvin Some remarks on a paper of Aronszajn and Panitchpakdi. Pacific J. Math. 7 (1957), 1619–1621. (PDF)
- Henriksen, Melvin On minimal completely regular spaces associated with a given ring of continuous functions. Michigan Math. J. 4 (1957), 61–64. (PDF)
- Correl, Ellen; Henriksen, Melvin On rings of bounded continuous functions with values in a division ring. Proc. Amer. Math. Soc. 7 (1956), 194–198. (PDF)
- Henriksen, Melvin On the equivalence of the ring, lattice, and semigroup of continuous functions. Proc. Amer. Math. Soc. 7 (1956), 959–960. (PDF)
- Gillman, Leonard; Henriksen, Melvin Rings of continuous functions in which every finitely generated ideal is principal. Trans. Amer. Math. Soc. 82 (1956), 366–391. (PDF)
- Gillman, Leonard; Henriksen, Melvin Some remarks about elementary divisor rings. Trans. Amer. Math. Soc. 82 (1956), 362–365. (PDF)
- Henriksen, Melvin Some remarks on elementary divisor rings. II. Michigan Math. J. 3 (1955–1956), 159–163. (PDF)
- Erdös, P.; Gillman, L.; Henriksen, M. An isomorphism theorem for real-closed fields. Ann. of Math. (2) 61, (1955). 542–554. (PDF)
- Gillman, L.; Henriksen, M.; Jerison, M. On a theorem of Gelfand and Kolmogoroff concerning maximal ideals in rings of continuous functions. Proc. Amer. Math. Soc. 5, (1954). 447–455. (PDF)
- Gillman, Leonard; Henriksen, Melvin Concerning rings of continuous functions. Trans. Amer. Math. Soc. 77, (1954). 340–362. (PDF)
- Henriksen, Melvin On the prime ideals of the ring of entire functions. Pacific J. Math. 3, (1953). 711–720. (PDF)
- Henriksen, Melvin On rings of entire functions of finite order. J. Indian Math. Soc. (N.S.) 17, (1953). 59–61. (PDF)
- Henriksen, Melvin; Isbell, J. R. On the continuity of the real roots of an algebraic equation. Proc. Amer. Math. Soc. 4, (1953). 431–434. (PDF)
- Henriksen, Melvin On the ideal structure of the ring of entire functions. Pacific J. Math. 2, (1952). 179–184. (PDF)
Other publications
- Review of Dimension and Extensions by J.M. Aarts and T. Nishiura, Bull Amer. Math. Soc. 30 (1994), 282–284. (PDF)
- There are too many B.A.D. Mathematicians, The Mathematical Intelligencer 15, (1993), 6–9. (PDF)
- What they didn't tell me about calculus and the computer, UME Trends 5 (1992). (PDF)
- You can and should let your students to write in sentences, using writing to Teach Mathematics, MAA Notes 17 (1990), 50–52.
- Review of Extensions and Absolutes of Hausdorff Spaces by J.R. Porter and R.G. Woods, Bull. Amer. Math. Soc. 21 (1989), 168–171. (PDF)
- What is the Mathematics Clinic? Mathematics in College, City University of New York, Fall–Winter (1988), 52–55.
- Carry your coals to where they are needed, Prof. Stein, Humanistic Newsletter II (1988), Harvey Mudd College.
- Review of I Want to be a Mathematician: An Automathography by P. R. Halmos Historia Math. 14 (1987), 200–203. (PDF)
- Who cares if you wait? Or, is it true that we can't afford to save money on our jury system? Town Hall Reporter, March, 1979.
- Applying mathematics without a license, Amer. Math. Monthly, 84 (1977), 648–650. (PDF)
- Henriksen, Melvin and G. Orland, On the juror utilization problem, Jurimetrics J. 16 (1976), 318–333. (PDF)
- Calculus and the Computer: A Conservative Approach, Proceedings of the Conference on Computers in the Undergraduate Curricula, University of Iowa (June 1970), 412–415. (PDF)