A pseudocompact Tychonoff space all countable subsets of which are closed and \(C^*\)-embedded (Q1071339)
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scientific article; zbMATH DE number 3940218
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A pseudocompact Tychonoff space all countable subsets of which are closed and \(C^*\)-embedded |
scientific article; zbMATH DE number 3940218 |
Statements
A pseudocompact Tychonoff space all countable subsets of which are closed and \(C^*\)-embedded (English)
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1986
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Let X be a Tikhonov space and let all subsets of cardinality \(\leq \tau\) of X be closed (and \(C^*\)-embedded). Then X can be embedded as a closed subspace in a pseudocompact Tikhonov space Y such that all subsets of cardinality \(\leq \tau\) of Y are closed (and \(C^*\)-embedded). As an application of this result we construct a pseudocompact connected left- separated Tikhonov space having all its subsets of cardinality \(\leq \tau\) closed and \(C^*\)-embedded.
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diagonal of mapping
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cardinality of subsets
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axioms beyond ZFC
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pseudocompact Tikhonov space
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pseudocompact connected left-separated Tikhonov space
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