Mutually Compactificable Topological Spaces
Two disjoint topological spaces X, Y are (T2-) mutually compactificable if there exists a compact (T2-) topology on K=X∪Y which coincides on X, Y with their original topologies such that the points x∈X, y∈Y have open disjoint neighborhoods in K. This paper, the first one from a series, contains some...
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| Format: | Article |
| Language: | English |
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Wiley
2007-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2007/70671 |
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| author | Martin Maria Kovár |
| author_facet | Martin Maria Kovár |
| author_sort | Martin Maria Kovár |
| collection | DOAJ |
| description | Two disjoint topological spaces X, Y are (T2-) mutually compactificable if there exists a compact (T2-) topology on K=X∪Y which coincides on X, Y with their original topologies such that the points x∈X, y∈Y have open disjoint neighborhoods in K. This paper, the first one from a series, contains some initial investigations of the notion. Some key properties are the following: a topological space is mutually compactificable with some space if and only if it is θ-regular. A regular space on which every real-valued continuous function
is constant is mutually compactificable with no
S2-space. On the other hand, there exists a regular non-T3.5 space which is mutually compactificable with the infinite countable
discrete space. |
| format | Article |
| id | doaj-art-4c7d216dae064da78c37d34dd862603f |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2007-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-4c7d216dae064da78c37d34dd862603f2025-02-03T05:45:09ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252007-01-01200710.1155/2007/7067170671Mutually Compactificable Topological SpacesMartin Maria Kovár0Department of Mathematics, Faculty of Electrical Engineering and Communication, University of Technology, Technická 8, Brno 616 69, Czech RepublicTwo disjoint topological spaces X, Y are (T2-) mutually compactificable if there exists a compact (T2-) topology on K=X∪Y which coincides on X, Y with their original topologies such that the points x∈X, y∈Y have open disjoint neighborhoods in K. This paper, the first one from a series, contains some initial investigations of the notion. Some key properties are the following: a topological space is mutually compactificable with some space if and only if it is θ-regular. A regular space on which every real-valued continuous function is constant is mutually compactificable with no S2-space. On the other hand, there exists a regular non-T3.5 space which is mutually compactificable with the infinite countable discrete space.http://dx.doi.org/10.1155/2007/70671 |
| spellingShingle | Martin Maria Kovár Mutually Compactificable Topological Spaces International Journal of Mathematics and Mathematical Sciences |
| title | Mutually Compactificable Topological Spaces |
| title_full | Mutually Compactificable Topological Spaces |
| title_fullStr | Mutually Compactificable Topological Spaces |
| title_full_unstemmed | Mutually Compactificable Topological Spaces |
| title_short | Mutually Compactificable Topological Spaces |
| title_sort | mutually compactificable topological spaces |
| url | http://dx.doi.org/10.1155/2007/70671 |
| work_keys_str_mv | AT martinmariakovar mutuallycompactificabletopologicalspaces |