Degenerate fibres in the Stone-Cech compactification of the universal bundle of a finite group
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Degenerate Fibres in the Stone-čech Compactification of the Universal Bundle of a Finite Group
Applied to a continuous surjection π : E → B of completely regular Hausdorff spaces E and B, the Stone-Čech compactification functor β yields a surjection βπ : βE → βB. For an n-fold covering map π, we show that the fibres of βπ, while never containing more than n points, may degenerate to sets of cardinality properly dividing n. In the special case of the universal bundle π : EG → BG of a p-gr...
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If p : E → B is a continuous surjection between completely regular spaces E and B, we may apply the Stone-Čech compactification functor β to obtain a surjection βp : βE → βB. It is well-known that if E = B × F where F is a finite set and p is projection on the first factor, then βE = βB × βF , and βp is again projection on the first factor. In this paper, we apply β to an n-fold covering map, t...
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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...
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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...
متن کاملApplications of the Stone-cech Compactification to Free Topological Groups
In this note the Stone-Cech compactification is used to produce short proofs of two theorems on the structure of free topological groups. The first is: The free topological group on any Tychonoff space X contains, as a closed subspace, a homeomorphic copy of the product space X". This is a generalization of a result of B. V. S. Thomas. The second theorem proved is C. Joiner's, Fundamental Lemma.
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2002
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-02-03008-8