Condensations of Cartesian products
Pavlov, Oleg I.
Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999), p. 355-365 / Harvested from Czech Digital Mathematics Library
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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.

Publié le : 1999-01-01
Classification:  54A10,  54B10,  54C10 
@article{119092,
     author = {Oleg I. Pavlov},
     title = {Condensations of Cartesian products},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {40},
     year = {1999},
     pages = {355-365},
     zbl = {0976.54008},
     mrnumber = {1732657},
     language = {en},
     url = {http://dml.mathdoc.fr/item/119092}
}

Pavlov, Oleg I. Condensations of Cartesian products. Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) pp. 355-365. http://gdmltest.u-ga.fr/item/119092/

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