Wallman-type Compactifications
نویسندگان
چکیده
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 iff T = w£y for each dense YQTwhere T7££. From these theorems we show that every compact .F-space and every compact orderable space is a Wallman compactification of each of its dense subspaces.
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