ω H-sets and cardinal invariants

Alessandro Fedeli

Commentationes Mathematicae Universitatis Carolinae (1998)

  • Volume: 39, Issue: 2, page 367-370
  • ISSN: 0010-2628

Abstract

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A subset A of a Hausdorff space X is called an ω H-set in X if for every open family 𝒰 in X such that A ⊂ ⋃ 𝒰 there exists a countable subfamily 𝒱 of 𝒰 such that A ⊂ ⋃ { V ¯ : V ∈ 𝒱 } . In this paper we introduce a new cardinal function t s θ and show that | A | ≤ 2 t s θ ( X ) ψ c ( X ) for every ω H-set A of a Hausdorff space X .

How to cite

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Fedeli, Alessandro. "$\omega $H-sets and cardinal invariants." Commentationes Mathematicae Universitatis Carolinae 39.2 (1998): 367-370. <http://eudml.org/doc/248228>.

@article{Fedeli1998,
abstract = {A subset $A$ of a Hausdorff space $X$ is called an $\omega $H-set in $X$ if for every open family $\mathcal \{U\}$ in $X$ such that $A \subset \bigcup \mathcal \{U\}$ there exists a countable subfamily $\mathcal \{V\}$ of $\mathcal \{U\}$ such that $A \subset \bigcup \lbrace \overline\{V\} : V \in \mathcal \{V\} \rbrace $. In this paper we introduce a new cardinal function $t_\{s\theta \}$ and show that $|A| \le 2^\{t_\{s\theta \}(X)\psi _\{c\}(X)\}$ for every $\omega $H-set $A$ of a Hausdorff space $X$.},
author = {Fedeli, Alessandro},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {cardinal function; $\omega $H-set; cardinal function of a topological space; H-set; closed pseudocharacter of a space},
language = {eng},
number = {2},
pages = {367-370},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {$\omega $H-sets and cardinal invariants},
url = {http://eudml.org/doc/248228},
volume = {39},
year = {1998},
}

TY - JOUR
AU - Fedeli, Alessandro
TI - $\omega $H-sets and cardinal invariants
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1998
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 39
IS - 2
SP - 367
EP - 370
AB - A subset $A$ of a Hausdorff space $X$ is called an $\omega $H-set in $X$ if for every open family $\mathcal {U}$ in $X$ such that $A \subset \bigcup \mathcal {U}$ there exists a countable subfamily $\mathcal {V}$ of $\mathcal {U}$ such that $A \subset \bigcup \lbrace \overline{V} : V \in \mathcal {V} \rbrace $. In this paper we introduce a new cardinal function $t_{s\theta }$ and show that $|A| \le 2^{t_{s\theta }(X)\psi _{c}(X)}$ for every $\omega $H-set $A$ of a Hausdorff space $X$.
LA - eng
KW - cardinal function; $\omega $H-set; cardinal function of a topological space; H-set; closed pseudocharacter of a space
UR - http://eudml.org/doc/248228
ER -

References

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