# Isaac Namioka

**Isaac Namioka** (born April 25, 1928)^{[1]} is a Japanese-American mathematician who has worked in general topology and functional analysis. He is a professor emeritus of mathematics at the University of Washington.^{[2]}

## Early life and education

Namioka was born in Tōno, not far from Namioka in the north of Honshu, Japan. When he was young his parents moved farther south, to Himeji.^{[3]}
He attended graduate school at the University of California, Berkeley, earning a doctorate in 1956 under the supervision of John L. Kelley.^{[4]} As a graduate student, Namioka married Chinese-American mathematics student Lensey Namioka, later to become a well-known novelist who used Namioka's Japanese heritage in some of her novels.^{[3]}

## Career

Namioka taught at Cornell University until 1963, when he moved to the University of Washington.^{[1]} There he was the doctoral advisor to four students. He has over 20 academic descendants, largely through his student Joseph Rosenblatt, who became a professor at the University of Illinois at Urbana–Champaign.^{[4]}

## Contributions

Namioka's book *Linear Topological Spaces* with Kelley has become a "standard text".^{[1]} However, although his doctoral work and this book both concerned general topology, his interests later shifted to functional analysis.^{[5]}

With Asplund in 1967, Namioka gave one of the first complete proofs of the Ryll-Nardzewski fixed-point theorem.^{[6]}

Following his 1974 paper "separate continuity and joint continuity", a Namioka space has come to mean a topological space *X* with the property that whenever *Y* is a compact space and function *f* from the Cartesian product of *X* and *Y* to *Z* is separately continuous in *X* and *Y*, there must exist a dense *G _{δ}* set within

*X*whose Cartesian product with

*Y*is a subset of the set of points of continuity of

*f*.

^{[7]}

^{[8]}The result of the 1974 paper, a proof of this property for a specific class of topological spaces, has come to be known as Namioka's theorem.

^{[9]}

In 1975, Namioka and Phelps established one side of the theorem that a space is an Asplund space if and only if its dual space has the Radon–Nikodým property. The other side was completed in 1978 by Stegall.^{[10]}

## Awards and honors

A special issue of the *Journal of Mathematical Analysis and Applications* was dedicated to Namioka to honor his 80th birthday.^{[1]}
In 2012, he became one of the inaugural fellows of the American Mathematical Society.^{[11]}

## Selected publications

- Books

*Partially Ordered Linear Topological Spaces*(Memoirs of the American Mathematical Society 14, 1957)^{[12]}*Linear Topological Spaces*(with John L. Kelley, Van Nostrand, 1963; Graduate Texts in Mathematics 36, Springer-Verlag, 1976)^{[13]}^{[14]}

- Research papers

- Namioka, I.; Asplund, E. (1967), "A geometric proof of Ryll-Nardzewski's fixed point theorem",
*Bulletin of the American Mathematical Society*,**73**: 443–445, doi:10.1090/s0002-9904-1967-11779-8, MR 0209904. - Namioka, I. (1974), "Separate continuity and joint continuity",
*Pacific Journal of Mathematics*,**51**: 515–531, doi:10.2140/pjm.1974.51.515, MR 0370466. - Namioka, I.; Phelps, R. R. (1975), "Banach spaces which are Asplund spaces",
*Duke Mathematical Journal*,**42**(4): 735–750, doi:10.1215/s0012-7094-75-04261-1, MR 0390721.

## References

- 1 2 3 4 Cascales, Bernardo; Godefroy, Gilles; Orihuela, José; Phelps, Robert (2009), "Preface: The interplay between measure theory, topology, and functional analysis" (PDF),
*Journal of Mathematical Analysis and Applications*,**350**(2): 425–426, doi:10.1016/j.jmaa.2008.10.035, MR 2474777. - ↑ Faculty profile, Univ. of Washington, retrieved 2015-01-24.
- 1 2 Wakan, Naomi,
*Interview with Lensey Namioka*, papertigers.org, retrieved 2015-01-24. - 1 2 Isaac Namioka at the Mathematics Genealogy Project
- ↑ Beery, Janet; Mead, Carol (January 2012), "Who's That Mathematician? Paul R. Halmos Collection - Page 37",
*Loci*, Mathematical Association of America, doi:10.4169/loci003801. - ↑ Granas, Andrzej; Dugundji, James (2003),
*Fixed Point Theory*, Springer Monographs in Mathematics, Springer-Verlag, New York, p. 196, doi:10.1007/978-0-387-21593-8, ISBN 0-387-00173-5, MR 1987179. - ↑ Lee, J. P.; Piotrowski, Z. (1985), "A note on spaces related to Namioka spaces",
*Bulletin of the Australian Mathematical Society*,**31**(2): 285–292, doi:10.1017/S0004972700004755, MR 788582. - ↑ Hazewinkel, Michiel, ed. (2001), "Namioka space",
*Encyclopedia of Mathematics*, Springer, ISBN 978-1-55608-010-4 - ↑ Hazewinkel, Michiel, ed. (2001), "Namioka theorem",
*Encyclopedia of Mathematics*, Springer, ISBN 978-1-55608-010-4 - ↑ Giles, J. R. (1982), "On the characterisation of Asplund spaces",
*Journal of the Australian Mathematical Society*, Series A,**32**(1): 134–144, doi:10.1017/s1446788700024472, MR 643437. - ↑ List of Fellows of the American Mathematical Society, retrieved 2015-01-24.
- ↑ Review of
*Partially Ordered Linear Topological Spaces*by Victor Klee, MR 0094681. - ↑ Review of 1963 ed. of
*Linear Topological Spaces*by Richard Friederich Arens, MR 0166578. For the 1976 ed. see MR 0394084. - ↑ West, T. T. (December 1964), "Kelley, J. L., Namioka, I., and others,
*Linear Topological Spaces*", Book Reviews,*Proceedings of the Edinburgh Mathematical Society*, Series 2,**14**(2): 168, doi:10.1017/S0013091500025931.