A regular topological space having no closed subsets of cardinality n2

Martin Goldstern; Haim I. Judah; Saharon Shelah

doi:10.1090/S0002-9939-1991-1052572-9

A regular topological space having no closed subsets of cardinality n2

Martin Goldstern
, Haim I. Judah
, Saharon Shelah

Einstein Institute of Mathematics

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

Abstract

Using ◊_λ⁺, we construct a regular topological space in which all closed sets are of cardinality either < λ or ≥ 2.In particular (answering a question of Juhász) there is always a regular space in which no closed set has cardinality N₂.

Original language	English
Pages (from-to)	1151-1159
Number of pages	9
Journal	Proceedings of the American Mathematical Society
Volume	111
Issue number	4
DOIs	https://doi.org/10.1090/S0002-9939-1991-1052572-9
State	Published - Apr 1991

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title = "A regular topological space having no closed subsets of cardinality n2",

abstract = "Using ◊λ+, we construct a regular topological space in which all closed sets are of cardinality either < λ or ≥ 2.In particular (answering a question of Juh{\'a}sz) there is always a regular space in which no closed set has cardinality N2.",

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A regular topological space having no closed subsets of cardinality n2

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