Displaying similar documents to “On ω * -closed sets and their topology.”

Eberlein spaces of finite metrizability number

István Juhász, Zoltán Szentmiklóssy, Andrzej Szymański (2007)

Commentationes Mathematicae Universitatis Carolinae

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Yakovlev [, Comment. Math. Univ. Carolin. (1980), 263–283] showed that any Eberlein compactum is hereditarily σ -metacompact. We show that this property actually characterizes Eberlein compacta among compact spaces of finite metrizability number. Uniformly Eberlein compacta and Corson compacta of finite metrizability number can be characterized in an analogous way.

Algebras of Borel measurable functions

Michał Morayne (1992)

Fundamenta Mathematicae

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We determine the size levels for any function on the hyperspace of an arc as follows. Assume Z is a continuum and consider the following three conditions: 1) Z is a planar AR; 2) cut points of Z have component number two; 3) any true cyclic element of Z contains at most two cut points of Z. Then any size level for an arc satisfies 1)-3) and conversely, if Z satisfies 1)-3), then Z is a diameter level for some arc.

A generic theorem in the theory of cardinal invariants of topological spaces

Aleksander V. Arhangel'skii (1995)

Commentationes Mathematicae Universitatis Carolinae

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Relative versions of many important theorems on cardinal invariants of topological spaces are formulated and proved on the basis of a general technical result, which provides an algorithm for such proofs. New relative cardinal invariants are defined, and open problems are discussed.