On closures of discrete sets

Santi Spadaro

doi:10.2989/16073606.2019.1617364

On closures of discrete sets

Santi Spadaro

Research output: Contribution to journal › Article › peer-review

Abstract

The depth of a topological space X (g(X)) is defined as the supremum of the cardinalities of closures of discrete subsets of X. Solving a problem of Martínez-Ruiz, Ramírez-Páramo and Romero-Morales, we prove that the cardinal inequality |X| ≤ g(X) ^L^(X)^F^(X) holds for every Hausdorﬀ space X, where L(X) is the Lindelöof number of X and F (X) is the supremum of the cardinalities of the free sequences in X.

Original language	English
Pages (from-to)	717-720
Number of pages	4
Journal	Quaestiones Mathematicae
Volume	44
Issue number	6
DOIs	https://doi.org/10.2989/16073606.2019.1617364
State	Published - 1 Jan 2021
Externally published	Yes

Keywords

Cardinal inequality
Lindelöf
depth
discrete set
elementary submodel

ASJC Scopus subject areas

Mathematics (miscellaneous)

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10.2989/16073606.2019.1617364

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KW - Lindelöf

KW - depth

KW - discrete set

KW - elementary submodel

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ER -

On closures of discrete sets

Abstract

Keywords

ASJC Scopus subject areas

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