The regular open-open topology for function spaces
The regular open-open topology, Troo, is introduced, its properties for spaces of continuous functions are discussed, and Troo is compared to Too, the open-open topology. It is then shown that Troo on H(X), the collection of all self-homeomorphisms on a topological space, (X,T), is equivalent to the...
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| Format: | Article |
| Language: | English |
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Wiley
1996-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171296000415 |
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| _version_ | 1832556288660209664 |
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| author | Kathryn F. Porter |
| author_facet | Kathryn F. Porter |
| author_sort | Kathryn F. Porter |
| collection | DOAJ |
| description | The regular open-open topology, Troo, is introduced, its properties for spaces of
continuous functions are discussed, and Troo is compared to Too, the open-open topology. It is then
shown that Troo on H(X), the collection of all self-homeomorphisms on a topological space, (X,T),
is equivalent to the topology induced on H(X) by a specific quasi-uniformity on X, when X is a
semi-regular space. |
| format | Article |
| id | doaj-art-a73292b232e3443598eeb9be8836077f |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1996-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-a73292b232e3443598eeb9be8836077f2025-02-03T05:45:54ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251996-01-0119229930210.1155/S0161171296000415The regular open-open topology for function spacesKathryn F. Porter0Department of Mathematical Sciences, Saint Mary's College of California, Moraga, CA 94575, USAThe regular open-open topology, Troo, is introduced, its properties for spaces of continuous functions are discussed, and Troo is compared to Too, the open-open topology. It is then shown that Troo on H(X), the collection of all self-homeomorphisms on a topological space, (X,T), is equivalent to the topology induced on H(X) by a specific quasi-uniformity on X, when X is a semi-regular space.http://dx.doi.org/10.1155/S0161171296000415compact-open topologyadmissible topologyopen-open topology quasi-uniformityregular open setsemi-regular spacetopological group. |
| spellingShingle | Kathryn F. Porter The regular open-open topology for function spaces International Journal of Mathematics and Mathematical Sciences compact-open topology admissible topology open-open topology quasi-uniformity regular open set semi-regular space topological group. |
| title | The regular open-open topology for function spaces |
| title_full | The regular open-open topology for function spaces |
| title_fullStr | The regular open-open topology for function spaces |
| title_full_unstemmed | The regular open-open topology for function spaces |
| title_short | The regular open-open topology for function spaces |
| title_sort | regular open open topology for function spaces |
| topic | compact-open topology admissible topology open-open topology quasi-uniformity regular open set semi-regular space topological group. |
| url | http://dx.doi.org/10.1155/S0161171296000415 |
| work_keys_str_mv | AT kathrynfporter theregularopenopentopologyforfunctionspaces AT kathrynfporter regularopenopentopologyforfunctionspaces |