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1991 AMS Math. Subj. Class.:Primary 54C10; Secondary 54F65We provide both a spectral and an internal characterizations of arbitrary !-favorable spaces with respect to co-zero sets. As a corollary we establish that any product of compact !-favorable spaces with respect to co-zero sets is also !-favorable with respect to co-zero sets. We also prove that every C* -embedded !-favorable with respect to co-zero sets subspace of an extremally disconnected space is extremally disconnected.
Following Malykhin, we say that a space is extraresolvable if contains a family of dense subsets such that and the intersection of every two elements of is nowhere dense, where is a nonempty open subset of is the dispersion character of . We show that, for every cardinal , there is a compact extraresolvable space of size and dispersion character . In connection with some cardinal inequalities, we prove the equivalence of the following statements: 1) , 2) is extraresolvable and...
A ballean is a set endowed with some family of balls in such a way that a ballean can be considered as an asymptotic counterpart of a uniform topological space. We introduce and study a new cardinal invariant of a ballean, the extraresolvability, which is an asymptotic reflection of the corresponding invariant of a topological space.
A class of closed, bounded, convex sets in the Banach space is shown to be a complete PCA set.
It has been an open question since 1997 whether, and under what assumptions on the underlying space, extreme topological measures are dense in the set of all topological measures on the space. The present paper answers this question. The main result implies that extreme topological measures are dense on a variety of spaces, including spheres, balls and projective planes.
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