# Condensations of Cartesian products

Commentationes Mathematicae Universitatis Carolinae (1999)

- Volume: 40, Issue: 2, page 355-365
- ISSN: 0010-2628

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topPavlov, Oleg I.. "Condensations of Cartesian products." Commentationes Mathematicae Universitatis Carolinae 40.2 (1999): 355-365. <http://eudml.org/doc/248401>.

@article{Pavlov1999,

abstract = {We consider when one-to-one continuous mappings can improve normality-type and compactness-type properties of topological spaces. In particular, for any Tychonoff non-pseudocompact space $X$ there is a $\mu $ such that $X^\mu $ can be condensed onto a normal ($\sigma $-compact) space if and only if there is no measurable cardinal. For any Tychonoff space $X$ and any cardinal $\nu $ there is a Tychonoff space $M$ which preserves many properties of $X$ and such that any one-to-one continuous image of $M^\mu $, $\mu \le \nu $, contains a closed copy of $X^\mu $. For any infinite compact space $K$ there is a normal space $X$ such that $X\times K$ cannot be mapped one-to-one onto a normal space.},

author = {Pavlov, Oleg I.},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {condensation; one-to-one; compact; measurable; topologies on product; compact space; measurable cardinal},

language = {eng},

number = {2},

pages = {355-365},

publisher = {Charles University in Prague, Faculty of Mathematics and Physics},

title = {Condensations of Cartesian products},

url = {http://eudml.org/doc/248401},

volume = {40},

year = {1999},

}

TY - JOUR

AU - Pavlov, Oleg I.

TI - Condensations of Cartesian products

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 1999

PB - Charles University in Prague, Faculty of Mathematics and Physics

VL - 40

IS - 2

SP - 355

EP - 365

AB - We consider when one-to-one continuous mappings can improve normality-type and compactness-type properties of topological spaces. In particular, for any Tychonoff non-pseudocompact space $X$ there is a $\mu $ such that $X^\mu $ can be condensed onto a normal ($\sigma $-compact) space if and only if there is no measurable cardinal. For any Tychonoff space $X$ and any cardinal $\nu $ there is a Tychonoff space $M$ which preserves many properties of $X$ and such that any one-to-one continuous image of $M^\mu $, $\mu \le \nu $, contains a closed copy of $X^\mu $. For any infinite compact space $K$ there is a normal space $X$ such that $X\times K$ cannot be mapped one-to-one onto a normal space.

LA - eng

KW - condensation; one-to-one; compact; measurable; topologies on product; compact space; measurable cardinal

UR - http://eudml.org/doc/248401

ER -

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