Displaying similar documents to “A generic theorem in the theory of cardinal invariants of topological spaces”

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.

Relatively compact spaces and separation properties

Aleksander V. Arhangel'skii, Ivan V. Yashchenko (1996)

Commentationes Mathematicae Universitatis Carolinae

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We consider the property of relative compactness of subspaces of Hausdorff spaces. Several examples of relatively compact spaces are given. We prove that the property of being a relatively compact subspace of a Hausdorff spaces is strictly stronger than being a regular space and strictly weaker than being a Tychonoff space.

The fixed point set of open mappings on extremally disconnected spaces

Egbert Thümmel (1994)

Commentationes Mathematicae Universitatis Carolinae

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We give an example of an extremally disconnected compact Hausdorff space with an open continuous selfmap such that the fixed point set is nonvoid and nowhere dense, respṫhat there is exactly one nonisolated fixed point.

Ordered spaces with special bases

Harold Bennett, David Lutzer (1998)

Fundamenta Mathematicae

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We study the roles played by four special types of bases (weakly uniform bases, ω-in-ω bases, open-in-finite bases, and sharp bases) in the classes of linearly ordered and generalized ordered spaces. For example, we show that a generalized ordered space has a weakly uniform base if and only if it is quasi-developable and has a G δ -diagonal, that a linearly ordered space has a point-countable base if and only if it is first-countable and has an ω-in-ω base, and that metrizability in a generalized...