On Hausdorff compactifications of non-locally compact spaces
Let X be a completely regular, Hausdorff space and let R be the set of points in X which do not possess compact neighborhoods. Assume R is compact. If X has a compactification with a countable remainder, then so does the quotient X/R, and a countable compactificatlon of X/R implies one for X−R. A ch...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
1979-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171279000375 |
| Summary: | Let X be a completely regular, Hausdorff space and let R be the set of points in X which do not possess compact neighborhoods. Assume R is compact. If X has a compactification with a countable remainder, then so does the quotient X/R, and a countable compactificatlon of X/R implies one for X−R. A characterization of when X/R has a compactification with a countable remainder is obtained. Examples show that the above implications cannot be reversed. |
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| ISSN: | 0161-1712 1687-0425 |