Two cardinal inequalities for functionally Hausdorff spaces

Alessandro Fedeli

Displaying similar documents to “Two cardinal inequalities for functionally Hausdorff spaces”

On the cardinality of functionally Hausdorff spaces

Alessandro Fedeli (1996)

Commentationes Mathematicae Universitatis Carolinae

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In this paper two new cardinal functions are introduced and investigated. In particular the following two theorems are proved: (i) If $X$ is a functionally Hausdorff space then $| X | \leq 2^{f s (X) ψ_{τ} (X)}$ ; (ii) Let $X$ be a functionally Hausdorff space with $f s (X) \leq κ$ . Then there is a subset $S$ of $X$ such that $| S | \leq 2^{κ}$ and $X = ⋃ {c l_{τ θ} (A) : A \in {[S]}^{\leq κ}}$ .

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.

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.

On the cardinality of Hausdorff spaces.

Fedeli, A. (1998)

Commentationes Mathematicae Universitatis Carolinae

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Local cardinal functions of H-closed spaces

Angelo Bella, Jack R. Porter (1996)

Commentationes Mathematicae Universitatis Carolinae

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The cardinal functions of pseudocharacter, closed pseudocharacter, and character are used to examine H-closed spaces and to contrast the differences between H-closed and minimal Hausdorff spaces. An H-closed space $X$ is produced with the properties that $| X | > 2^{2^{ψ (X)}}$ and $\bar{ψ} (X) > 2^{ψ (X)}$ .