A pseudocompact Tychonoff space all countable subsets of which are closed and C1-embedded |
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Affiliation: | Chair of General Topology and Geometry, Department of Mechanics and Mathematics, Moscow State University, 119 899 Moscow, USSR |
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Abstract: | Let X be a Tychonoff space and let all subsets of cardinality ⩽τ of X be closed (and C1-embedded). Then X can be embedded as a closed subspace in a pseudocompact Tychonoff space Y such that all subsets of cardinality ⩽τ of Y are closed (and C1-embedded). As an application of this result we construct a pseudocompact connected left-separated Tychonoff space having all its subsets of cardinality ⩽τ closed and C1-embedded. |
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