Neighborhood spaces
Neighborhood spaces, pretopological spaces, and closure spaces are topological space generalizations which can be characterized by means of their associated interior (or closure) operators. The category NBD of neighborhood spaces and continuous maps contains PRTOP as a bicoreflective subcategory and...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2002-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171202202203 |
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| _version_ | 1832556963429351424 |
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| author | D. C. Kent Won Keun Min |
| author_facet | D. C. Kent Won Keun Min |
| author_sort | D. C. Kent |
| collection | DOAJ |
| description | Neighborhood spaces, pretopological spaces, and closure spaces are topological space generalizations which can be characterized by means of their associated interior (or closure) operators. The category NBD of neighborhood spaces and continuous maps contains PRTOP as a bicoreflective subcategory and CLS as a bireflective subcategory, whereas TOP is bireflectively embedded in PRTOP and
bicoreflectively embedded in CLS. Initial and final structures are described in these categories, and it is shown that the Tychonov theorem holds in all of them. In order to describe a successful convergence theory in NBD, it is necessary to replace filters by
more general p-stacks. |
| format | Article |
| id | doaj-art-8f0fd6d1824d4a0da2ca2fcd6fdf24df |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2002-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-8f0fd6d1824d4a0da2ca2fcd6fdf24df2025-02-03T05:43:56ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252002-01-0132738739910.1155/S0161171202202203Neighborhood spacesD. C. Kent0Won Keun Min1Department of Mathematics, Washington State University, Pullman 99164-3113, WA, USADepartment of Mathematics, Kangwon National University, Chuncheon 200-701, KoreaNeighborhood spaces, pretopological spaces, and closure spaces are topological space generalizations which can be characterized by means of their associated interior (or closure) operators. The category NBD of neighborhood spaces and continuous maps contains PRTOP as a bicoreflective subcategory and CLS as a bireflective subcategory, whereas TOP is bireflectively embedded in PRTOP and bicoreflectively embedded in CLS. Initial and final structures are described in these categories, and it is shown that the Tychonov theorem holds in all of them. In order to describe a successful convergence theory in NBD, it is necessary to replace filters by more general p-stacks.http://dx.doi.org/10.1155/S0161171202202203 |
| spellingShingle | D. C. Kent Won Keun Min Neighborhood spaces International Journal of Mathematics and Mathematical Sciences |
| title | Neighborhood spaces |
| title_full | Neighborhood spaces |
| title_fullStr | Neighborhood spaces |
| title_full_unstemmed | Neighborhood spaces |
| title_short | Neighborhood spaces |
| title_sort | neighborhood spaces |
| url | http://dx.doi.org/10.1155/S0161171202202203 |
| work_keys_str_mv | AT dckent neighborhoodspaces AT wonkeunmin neighborhoodspaces |