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Isaac Namioka
Isaac Namioka (April 25, 1928 - September 25, 2019) was a Japanese-American mathematician who worked in general topology and functional analysis. He was a professor emeritus of mathematics at the University of Washington. 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, Japan. When he was young his parents moved farther south, to Himeji.. He attended graduate school at the University of California, Berkeley, earning a doctorate in 1956 under the supervision of John L. Kelley. 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. Career Namioka taught at Cornell University until 1963, when he moved to the University of Washington. There he was the doctoral advisor to four students. He has over 20 academic descendants, largely through his student J ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Isaac Namioka MFO
Isaac; grc, Ἰσαάκ, Isaák; ar, إسحٰق/إسحاق, Isḥāq; am, ይስሐቅ is one of the three patriarchs (Bible), patriarchs of the Israelites and an important figure in the Abrahamic religions, including Judaism, Christianity, and Islam. He was the son of Abraham and Sarah, the father of Jacob and Esau, and the grandfather of the Twelve Tribes of Israel, twelve tribes of Israel. Isaac's name means "he will laugh", reflecting the laughter, in disbelief, of Abraham and Sarah, when told by God that they would have a child., He is the only patriarch whose name was not changed, and the only one who did not move out of Canaan. According to the narrative, he died aged 180, the longest-lived of the three patriarchs. Etymology The anglicized name "Isaac" is a transliteration of the Hebrew name () which literally means "He laughs/will laugh." Ugaritic language, Ugaritic texts dating from the 13th century BCE refer to the benevolent smile of the Canaanite religion, Canaa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ryll-Nardzewski Fixed-point Theorem
In functional analysis, a branch of mathematics, the Ryll-Nardzewski fixed-point theorem states that if E is a normed vector space and K is a nonempty convex subset of E that is compact under the weak topology, then every group (or equivalently: every semigroup) of affine isometries of K has at least one fixed point. (Here, a ''fixed point'' of a set of maps is a point that is fixed by each map in the set.) This theorem was announced by Czesław Ryll-Nardzewski. Later Namioka and Asplund gave a proof based on a different approach. Ryll-Nardzewski himself gave a complete proof in the original spirit. Applications The Ryll-Nardzewski theorem yields the existence of a Haar measure on compact groups. See also * Fixed-point theorems * Fixed-point theorems in infinite-dimensional spaces * Markov-Kakutani fixed-point theorem - abelian semigroup of continuous affine self-maps on compact convex set in a topological vector space has a fixed point References * Andrzej Granas and James Du ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 size (with variable numbers of pages). The GTM series is easily identified by a white band at the top of the book. The books in this series tend to be written at a more advanced level than the similar Undergraduate Texts in Mathematics series, although there is a fair amount of overlap between the two series in terms of material covered and difficulty level. List of books #''Introduction to Axiomatic Set Theory'', Gaisi Takeuti, Wilson M. Zaring (1982, 2nd ed., ) #''Measure and Category – A Survey of the Analogies between Topological and Measure Spaces'', John C. Oxtoby (1980, 2nd ed., ) #''Topological Vector Spaces'', H. H. Schaefer, M. P. Wolff (1999, 2nd ed., ) #''A Course in Homological Algebra'', Peter Hilton, Urs Stammbac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Victor Klee
Victor LaRue Klee, Jr. (September 18, 1925 – August 17, 2007) was a mathematician specialising in convex sets, functional analysis, analysis of algorithms, optimization, and combinatorics. He spent almost his entire career at the University of Washington in Seattle. Life Born in San Francisco, Vic Klee earned his B.A. degree in 1945 with high honors from Pomona College, majoring in mathematics and chemistry. He did his graduate studies, including a thesis on Convex Sets in Linear Spaces, and received his PhD in mathematics from the University of Virginia in 1949. After teaching for several years at the University of Virginia, he moved in 1953 to the University of Washington in Seattle, Washington, where he was a faculty member for 54 years. He died in Lakewood, Ohio. Research Klee wrote more than 240 research papers. He proposed Klee's measure problem and the art gallery problem. Kleetopes are also named after him, as is the Klee–Minty cube, which shows that the simpl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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, advocacy and other programs. The society is one of the four parts of the Joint Policy Board for Mathematics and a member of the Conference Board of the Mathematical Sciences. History The AMS was founded in 1888 as the New York Mathematical Society, the brainchild of Thomas Fiske, who was impressed by the London Mathematical Society on a visit to England. John Howard Van Amringe was the first president and Fiske became secretary. The society soon decided to publish a journal, but ran into some resistance, due to concerns about competing with the American Journal of Mathematics. The result was the ''Bulletin of the American Mathematical Society'', with Fiske as editor-in-chief. The de facto journal, as intended, was influential in in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 educational institutions, a fellow can be a member of a highly ranked group of teachers at a particular college or university or a member of the governing body in some universities (such as the Fellows of Harvard College); it can also be a specially selected postgraduate student who has been appointed to a post (called a fellowship) granting a stipend, research facilities and other privileges for a fixed period (usually one year or more) in order to undertake some advanced study or research, often in return for teaching services. In the context of research and development-intensive large companies or corporations, the title "fellow" is sometimes given to a small number of senior scientists and engineers. In the context of medical education in No ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Festschrift
In academia, a ''Festschrift'' (; plural, ''Festschriften'' ) is a book honoring a respected person, especially an academic, and presented during their lifetime. It generally takes the form of an edited volume, containing contributions from the honoree's colleagues, former pupils, and friends. ''Festschriften'' are often titled something like ''Essays in Honour of...'' or ''Essays Presented to... .'' Terminology The term, borrowed from German, and literally meaning 'celebration writing' (cognate with ''feast-script''), might be translated as "celebration publication" or "celebratory (piece of) writing". An alternative Latin term is (literally: 'book of friends'). A comparable book presented posthumously is sometimes called a (, 'memorial publication'), but this term is much rarer in English. A ''Festschrift'' compiled and published by electronic means on the internet is called a (pronounced either or ), a term coined by the editors of the late Boris Marshak's , ''Eran ud Aner ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Radon–Nikodym Property
In mathematics, the Bochner integral, named for Salomon Bochner, extends the definition of Lebesgue integral to functions that take values in a Banach space, as the limit of integrals of simple functions. Definition Let (X, \Sigma, \mu) be a measure space, and B be a Banach space. The Bochner integral of a function f : X \to B is defined in much the same way as the Lebesgue integral. First, define a simple function to be any finite sum of the form s(x) = \sum_^n \chi_(x) b_i where the E_i are disjoint members of the \sigma-algebra \Sigma, the b_i are distinct elements of B, and χE is the characteristic function of E. If \mu\left(E_i\right) is finite whenever b_i \neq 0, then the simple function is integrable, and the integral is then defined by \int_X \left sum_^n \chi_(x) b_i\right, d\mu = \sum_^n \mu(E_i) b_i exactly as it is for the ordinary Lebesgue integral. A measurable function f : X \to B is Bochner integrable if there exists a sequence of integrable simple functions s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 interested in the Fréchet differentiability properties of Lipschitz functions on Banach spaces. Equivalent definitions There are many equivalent definitions of what it means for a Banach space ''X'' to be an Asplund space: * ''X'' is Asplund if, and only if, every separable subspace ''Y'' of ''X'' has separable continuous dual space ''Y''∗. * ''X'' is Asplund if, and only if, every continuous convex function on any open convex subset ''U'' of ''X'' is Fréchet differentiable at the points of a dense ''G''''δ''-subset of ''U''. * ''X'' is Asplund if, and only if, its dual space ''X''∗ has the Radon–Nikodým property. This property was established by Namioka & Phelps in 1975 and Stegall in 1978. * ''X'' is Asplund if, and only if, ev ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gδ Set
In the mathematical field of topology, a Gδ set is a subset of a topological space that is a countable intersection of open sets. The notation originated in German with ''G'' for '' Gebiet'' (''German'': area, or neighbourhood) meaning open set in this case and for '' Durchschnitt'' (''German'': intersection).. Historically Gδ sets were also called inner limiting sets, but that terminology is not in use anymore. Gδ sets, and their dual, F sets, are the second level of the Borel hierarchy. Definition In a topological space a Gδ set is a countable intersection of open sets. The Gδ sets are exactly the level Π sets of the Borel hierarchy. Examples * Any open set is trivially a Gδ set. * The irrational numbers are a Gδ set in the real numbers \R. They can be written as the countable intersection of the open sets \^ (the superscript denoting the complement) where q is rational. * The set of rational numbers \Q is a Gδ set in \R. If \Q were the intersection of open set ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dense Set
In topology and related areas of mathematics, a subset ''A'' of a topological space ''X'' is said to be dense in ''X'' if every point of ''X'' either belongs to ''A'' or else is arbitrarily "close" to a member of ''A'' — for instance, the rational numbers are a dense subset of the real numbers because every real number either is a rational number or has a rational number arbitrarily close to it (see Diophantine approximation). Formally, A is dense in X if the smallest closed subset of X containing A is X itself. The of a topological space X is the least cardinality of a dense subset of X. Definition A subset A of a topological space X is said to be a of X if any of the following equivalent conditions are satisfied: The smallest closed subset of X containing A is X itself. The closure of A in X is equal to X. That is, \operatorname_X A = X. The interior of the complement of A is empty. That is, \operatorname_X (X \setminus A) = \varnothing. Every point in X either ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
