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

general topology In mathematics, general 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 differential topology, geometri ...

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 (e.g. inner product, norm, topology, etc.) and the linear functions defined o ...

. He was a

professor emeritus ''Emeritus'' (; female: ''emerita'') is an adjective used to designate a retired chair, professor, pastor, bishop, pope, director, president, prime minister, rabbi, emperor, or other person who has been "permitted to retain as an honorary title ...

of mathematics at the

University of Washington The University of Washington (UW, simply Washington, or informally U-Dub) is a public research university in Seattle, Washington. Founded in 1861, Washington is one of the oldest universities on the West Coast; it was established in Seattl ...

. 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 called , is the largest and most populous island of Japan. It is located south of Hokkaidō across the Tsugaru Strait, north of Shikoku across the Inland Sea, and northeast of Kyūshū across the Kanmon Straits. The island se ...

, 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 land-grant research university in Berkeley, California. Established in 1868 as the University of California, it is the state's first land-grant u ...

, 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 () ( or ; 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 ...

, 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 statutory land-grant research university based in Ithaca, New York. It is a member of the Ivy League. Founded in 1865 by Ezra Cornell and Andrew Dickson White, Cornell was founded with the intention to tea ...

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 (U of I, Illinois, University of Illinois, or UIUC) is a public land-grant research university in Illinois in the twin cities of Champaign and Urbana. It is the flagship institution of the Univer ...

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 by making precise the idea of a space having no "punctures" or "missing endpoints", ...

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 Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematically ...

''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 In mathematics — specifically, in functional analysis — an Asplund space or strong differentiability space is a type of well-behaved Banach space. Asplund spaces were introduced in 1968 by the mathematician Edgar Asplund, who was inter ...

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 Literature * ''Speci ...

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 concept whose exact meaning depends on context. In learned or professional societies, it refers to a privileged member who is specially elected in recognition of their work and achievements. Within the context of higher education ...

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) (ISSN 0072-5285) 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 ...

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

References

{{DEFAULTSORT:Namioka, Isaac 1928 births 2019 deaths People 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