Wallman-type compactifications on $0$-dimensional spaces
نویسندگان
چکیده
منابع مشابه
Wallman-type Compactifications
All spaces in this paper are Tychonoff. A Wallman base on a space X is a normal separating ring of closed subsets of X (see Steiner, Duke Math. J. 35 (1968), 269-276). Let T be a compact space and £ a Wallman base on T. For XCZT, define £x = {Ar)X\AE£}. Theorem 1. If X is a dense subspace of T, then T = w£x iff cItAHclrB = 0 whenever A, S£& and AC\B = 0. Theorem 2. T = w£xfor each dense XCZT if...
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In this paper, X denotes an arbitrary nonempty set, a lattice of subsets of X with ∅, X∈ , A( ) is the algebra generated by and M( ) is the set of nontrivial, finite, and finitely additive measures on A( ), and MR( ) is the set of elements of M( ) which are -regular. It is well known that any μ ∈M( ) induces a finitely additive measure μ̄ on an associated Wallman space. Whenever μ ∈MR( ), μ̄ is c...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1974
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1974-0339079-9