Subalgebras of B(l1) and the Stone-Cech compactification βN
نویسندگان
چکیده
منابع مشابه
On 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...
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.
متن کاملStone-cech Compactifications via Adjunctions
The Stone-Cech compactification of a space X is described by adjoining to X continuous images of the Stone-tech growths of a complementary pair of subspaces of X. The compactification of an example of Potoczny from [P] is described in detail. The Stone-Cech compactification of a completely regular space X is a compact Hausdorff space ßX in which X is dense and C*-embedded, i.e. every bounded re...
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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 1979
ISSN: 0022-1236
DOI: 10.1016/0022-1236(79)90039-9