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...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
1979-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171279000375 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832563546260504576 |
|---|---|
| author | James Hatzenbuhler Don A. Mattson |
| author_facet | James Hatzenbuhler Don A. Mattson |
| author_sort | James Hatzenbuhler |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-2062212a175f4fe187e80f1523fae7c6 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1979-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-2062212a175f4fe187e80f1523fae7c62025-02-03T01:13:13ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251979-01-012348148610.1155/S0161171279000375On Hausdorff compactifications of non-locally compact spacesJames Hatzenbuhler0Don A. Mattson1Department of Mathematics, Moorhead State University, Moorhead 56560, Minnesota, USADepartment of Mathematics, Moorhead State University, Moorhead 56560, Minnesota, USALet 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.http://dx.doi.org/10.1155/S0161171279000375countable remainderscompactifications non-locally compact spacescomponents of βX - X. |
| spellingShingle | James Hatzenbuhler Don A. Mattson On Hausdorff compactifications of non-locally compact spaces International Journal of Mathematics and Mathematical Sciences countable remainders compactifications non-locally compact spaces components of βX - X. |
| title | On Hausdorff compactifications of non-locally compact spaces |
| title_full | On Hausdorff compactifications of non-locally compact spaces |
| title_fullStr | On Hausdorff compactifications of non-locally compact spaces |
| title_full_unstemmed | On Hausdorff compactifications of non-locally compact spaces |
| title_short | On Hausdorff compactifications of non-locally compact spaces |
| title_sort | on hausdorff compactifications of non locally compact spaces |
| topic | countable remainders compactifications non-locally compact spaces components of βX - X. |
| url | http://dx.doi.org/10.1155/S0161171279000375 |
| work_keys_str_mv | AT jameshatzenbuhler onhausdorffcompactificationsofnonlocallycompactspaces AT donamattson onhausdorffcompactificationsofnonlocallycompactspaces |