Increasing chains and discrete reflection of cardinality

Santi Spadaro

Increasing chains and discrete reflection of cardinality

Santi Spadaro

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

2 Scopus citations

Abstract

Combining ideas from two of our previous papers ([26] and [27]), we refine Arhangel'skii Theorem by proving a cardinal inequality of which this is a special case: any increasing union of strongly discretely Lindel̈of spaces without uncountable free sequences and with countable pseudocharacter has cardinality at most continuum. We then give a partial positive answer to a problem of Alan Dow on reflection of cardinality by closures of discrete sets.

Original language	English
Pages (from-to)	73-82
Number of pages	10
Journal	Rendiconti dell'Istituto di Matematica dell'Universita di Trieste
Volume	45
Issue number	1
State	Published - 1 Dec 2013
Externally published	Yes

Keywords

Arhangel'skii theorem
Discrete set
Elementary submodel
Free sequence
Strongly discretely lindelöf

ASJC Scopus subject areas

General Mathematics

Cite this

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abstract = "Combining ideas from two of our previous papers ([26] and [27]), we refine Arhangel'skii Theorem by proving a cardinal inequality of which this is a special case: any increasing union of strongly discretely Linde{\"l}of spaces without uncountable free sequences and with countable pseudocharacter has cardinality at most continuum. We then give a partial positive answer to a problem of Alan Dow on reflection of cardinality by closures of discrete sets.",

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AB - Combining ideas from two of our previous papers ([26] and [27]), we refine Arhangel'skii Theorem by proving a cardinal inequality of which this is a special case: any increasing union of strongly discretely Lindel̈of spaces without uncountable free sequences and with countable pseudocharacter has cardinality at most continuum. We then give a partial positive answer to a problem of Alan Dow on reflection of cardinality by closures of discrete sets.

KW - Arhangel'skii theorem

KW - Discrete set

KW - Elementary submodel

KW - Free sequence

KW - Strongly discretely lindelöf

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Increasing chains and discrete reflection of cardinality

Abstract

Keywords

ASJC Scopus subject areas

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