Displaying similar documents to “On the cardinality of Hausdorff spaces.”

On the cardinality of Hausdorff spaces

Alessandro Fedeli (1998)

Commentationes Mathematicae Universitatis Carolinae

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The aim of this paper is to show, using the reflection principle, three new cardinal inequalities. These results improve some well-known bounds on the cardinality of Hausdorff spaces.

Two cardinal inequalities for functionally Hausdorff spaces

Alessandro Fedeli (1994)

Commentationes Mathematicae Universitatis Carolinae

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In this paper, two cardinal inequalities for functionally Hausdorff spaces are established. A bound on the cardinality of the τ θ -closed hull of a subset of a functionally Hausdorff space is given. Moreover, the following theorem is proved: if X is a functionally Hausdorff space, then | X | ≤ 2 χ ( X ) wcd ( X ) .

On the cardinality of n-Urysohn and n-Hausdorff spaces

Maddalena Bonanzinga, Maria Cuzzupé, Bruno Pansera (2014)

Open Mathematics

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Two variations of Arhangelskii’s inequality X ⩽ 2 χ ( X ) - L ( X ) for Hausdorff X [Arhangel’skii A.V., The power of bicompacta with first axiom of countability, Dokl. Akad. Nauk SSSR, 1969, 187, 967–970 (in Russian)] given in [Stavrova D.N., Separation pseudocharacter and the cardinality of topological spaces, Topology Proc., 2000, 25(Summer), 333–343] are extended to the classes with finite Urysohn number or finite Hausdorff number.