Book Review: The Stone-Čech compactification
نویسندگان
چکیده
منابع مشابه
Algebra in the Stone - Čech Compactification and its Applications to Ramsey Theory
Let me begin by expressing my sincere gratitude to the Japanese Association of Mathematical Sciences for inviting me to present this lecture and for giving me the JAMS International Prize for 2003 . I am deeply honored. This lecture is not a survey, but simply a discussion of some topics that I find interesting. For the most recent surveys of this subject area in which I have participated see [...
متن کاملThe Stone-Čech compactification of Tychonoff spaces
A topological space X is said to be completely regular if whenever F is a nonempty closed set and x ∈ X \F , there is a continuous function f : X → [0, 1] such that f(x) = 0 and f(F ) = {1}. A completely regular space need not be Hausdorff. For example, ifX is any set with more than one point, then the trivial topology, in which the only closed sets are ∅ and X, is vacuously completely regular,...
متن کاملStrong shape of the Stone-Čech compactification
J. Keesling has shown that for connected spaces X the natural inclusion e : X → βX of X in its Stone-Čech compactification is a shape equivalence if and only if X is pseudocompact. This paper establishes the analogous result for strong shape. Moreover, pseudocompact spaces are characterized as spaces which admit compact resolutions, which improves a result of I. Lončar.
متن کاملOn the existence of Stone-Cech compactification
Introduction. In 1937 E. Čech and M.H. Stone independently introduced the maximal compactification of a completely regular topological space, thereafter called Stone-Čech compactification [8, 18]. In the introduction of [8] the non-constructive character of this result is so described: “it must be emphasized that β(S) [the Stone-Čech compactification of S] may be defined only formally (not cons...
متن کاملA Stone-cech Compactification for Limit Spaces
O. Wyler [Notices Amer. Math. Soc. 15 (1968), 169. Abstract #653-306.] has given a Stone-Cech compactification for limit spaces. However, his is not necessarily an embedding. Here, it is shown that any Hausdorff limit space (X, t) can be embedded as a dense subspace of a compact, Hausdorff, limit space (Xi, ri) with the following property: any continuous function from (X, t) into a compact, Hau...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1976
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1976-14084-0