Condensations of Cartesian products
Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) no. 2, pp. 355-365
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library
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 $M^\mu$, $\mu\leq\nu$, 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.
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 $M^\mu$, $\mu\leq\nu$, 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.
@article{CMUC_1999_40_2_a17,
author = {Pavlov, Oleg},
title = {Condensations of {Cartesian} products},
journal = {Commentationes Mathematicae Universitatis Carolinae},
pages = {355--365},
year = {1999},
volume = {40},
number = {2},
mrnumber = {1732657},
zbl = {0976.54008},
language = {en},
url = {http://geodesic.mathdoc.fr/item/CMUC_1999_40_2_a17/}
}
Pavlov, Oleg. Condensations of Cartesian products. Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) no. 2, pp. 355-365. http://geodesic.mathdoc.fr/item/CMUC_1999_40_2_a17/