An independency result in connectification theory

Alessandro Fedeli; Attilio Le Donne

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 $X = ⋃ {c l_{τ θ} (A) : A \in {[S]}^{\leq κ}}$ .

Compacta are maximally $G_{δ}$ -resolvable

István Juhász, Zoltán Szentmiklóssy (2013)

Commentationes Mathematicae Universitatis Carolinae

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It is well-known that compacta (i.e. compact Hausdorff spaces) are maximally resolvable, that is every compactum $X$ contains $Δ (X)$ many pairwise disjoint dense subsets, where $Δ (X)$ denotes the minimum size of a non-empty open set in $X$ . The aim of this note is to prove the following analogous result: Every compactum $X$ contains $Δ_{δ} (X)$ many pairwise disjoint $G_{δ}$ -dense subsets, where $Δ_{δ} (X)$ denotes the minimum size of a non-empty $G_{δ}$ set in $X$ .

Displaying similar documents to “An independency result in connectification theory”

On the cardinality of functionally Hausdorff spaces

Compacta are maximally G δ -resolvable

Compacta are maximally $G_{δ}$ -resolvable