Isaac Namioka (April 25, 1928 – September 25, 2019) was a Japanese-American mathematician who worked in

general topology In mathematics, general topology (or point set topology) is the branch of topology that deals with the basic set-theoretic definitions and constructions used in topology. It is the foundation of most other branches of topology, including differ ...

and

functional analysis Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (for example, Inner product space#Definition, inner product, Norm (mathematics ...

. He was a

professor emeritus ''Emeritus/Emerita'' () is an honorary title granted to someone who retirement, retires from a position of distinction, most commonly an academic faculty position, but is allowed to continue using the previous title, as in "professor emeritus". ...

of mathematics at the

University of Washington The University of Washington (UW and informally U-Dub or U Dub) is a public research university in Seattle, Washington, United States. Founded in 1861, the University of Washington is one of the oldest universities on the West Coast of the Uni ...

. He died at home in Seattle on September 25, 2019.

Early life and education

Namioka was born in Tōno, not far from Namioka in the north of

Honshu , historically known as , is the largest of the four main islands of Japan. It lies between the Pacific Ocean (east) and the Sea of Japan (west). It is the list of islands by area, seventh-largest island in the world, and the list of islands by ...

, Japan. When he was young his parents moved farther south, to

Himeji 260px, Himeji City Hall is a city located in Hyōgo Prefecture in the Kansai region of Japan. , the city had an estimated population of 525,682 in 227,099 households and a population density of 980 persons per km2. The total area of the city is ...

.. He attended graduate school at the

University of California, Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California), is a Public university, public Land-grant university, land-grant research university in Berkeley, California, United States. Founded in 1868 and named after t ...

, earning a doctorate in 1956 under the supervision of John L. Kelley. As a graduate student, Namioka married Chinese-American mathematics student

Lensey Namioka Lensey Namioka () (; born June 14, 1929) is a Chinese-born American writer of books for young adults and children. She writes about China and Chinese American families, as well as Japan, her husband's native country. Early life and education L ...

, later to become a well-known novelist who used Namioka's Japanese heritage in some of her novels.

Career

Namioka taught at

Cornell University Cornell University is a Private university, private Ivy League research university based in Ithaca, New York, United States. The university was co-founded by American philanthropist Ezra Cornell and historian and educator Andrew Dickson W ...

until 1963, when he moved to the

. There he was the

doctoral advisor A doctoral advisor (also dissertation director, dissertation advisor; or doctoral supervisor) is a member of a university faculty whose role is to guide graduate students who are candidates for a doctorate, helping them select coursework, as well ...

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 The University of Illinois Urbana-Champaign (UIUC, U of I, Illinois, or University of Illinois) is a public land-grant research university in the Champaign–Urbana metropolitan area, Illinois, United States. Established in 1867, it is the f ...

Contributions

Namioka's book ''Linear Topological Spaces'' with Kelley has become a "standard text". Although his doctoral work and this book both concerned

, his interests later shifted to

. With Asplund in 1967, Namioka gave one of the first complete proofs of the Ryll-Nardzewski fixed-point theorem. 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 In mathematics, specifically general topology, compactness is a property that seeks to generalize the notion of a closed and bounded subset of Euclidean space. The idea is that a compact space has no "punctures" or "missing endpoints", i.e., i ...

and function ''f'' from the

Cartesian product In mathematics, specifically set theory, the Cartesian product of two sets and , denoted , is the set of all ordered pairs where is an element of and is an element of . In terms of set-builder notation, that is A\times B = \. A table c ...

of ''X'' and ''Y'' to ''Z'' is separately continuous in ''X'' and ''Y'', there must exist a

dense Density (volumetric mass density or specific mass) is the ratio of a substance's mass to its volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' (or ''d'') can also be use ...

''G_δ'' set within ''X'' whose Cartesian product with ''Y'' is a subset of the set of points of continuity of ''f''. 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. 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.

Awards and honors

special issue Special or specials may refer to: Policing * Specials, Ulster Special Constabulary, the Northern Ireland police force * Specials, Special Constable, an auxiliary, volunteer, or temporary; police worker or police officer * Special police forces M ...

of the ''Journal of Mathematical Analysis and Applications'' was dedicated to Namioka to honor his 80th birthday.. In 2012, he became one of the inaugural

fellow A fellow is a title and form of address for distinguished, learned, or skilled individuals in academia, medicine, research, and industry. The exact meaning of the term differs in each field. In learned society, learned or professional society, p ...

s of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

Selected publications

;Books *''Partially Ordered Linear Topological Spaces'' (Memoirs of the American Mathematical Society 14, 1957) *''Linear Topological Spaces'' (with John L. Kelley, Van Nostrand, 1963;

Graduate Texts in Mathematics Graduate Texts in Mathematics (GTM) () is a series of graduate-level textbooks in mathematics published by Springer-Verlag. The books in this series, like the other Springer-Verlag mathematics series, are yellow books of a standard size (with va ...

36, Springer-Verlag, 1976). ;Research papers *. *. *.

References

{{DEFAULTSORT:Namioka, Isaac 1928 births 2019 deaths People from Iwate Prefecture Scientists from Iwate Prefecture Japanese mathematicians Japanese emigrants to the United States 20th-century American mathematicians 21st-century American mathematicians Topologists Functional analysts University of California, Berkeley alumni Cornell University faculty University of Washington faculty Fellows of the American Mathematical Society American academics of Japanese descent