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The Baire-category
method in some compact extension problems
Elżbieta Pol |
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Vol. 122 (1986), No. 1, 197–210
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Abstract |
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We characterize metrizable separable spaces X such that almost every, in the sense of Baire category, embedding h of X into the Hilbert cube Iω provides a compact extension h(X) such that the remainder h(X) ∖ h(X) has certain dimensional property (for instance, is n-dimensional, countable-dimensional or “metrically weakly infinite-dimensional”). We obtain a characterization of metrizable separable spaces which have large transfinite dimension by means of compactifications. Two examples related to the results mentioned above are constructed. |
Mathematical Subject Classification 2000
Primary: 54F45
Secondary: 54D40
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Milestones
Received: 21 October 1983
Revised: 29 April 1985
Published: 1 March 1986
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Authors |
| Elżbieta Pol | |
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