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Separation axioms and subcategories of top
| Content Provider | Scilit |
|---|---|
| Author | Nakagawa, Ryosuke |
| Copyright Year | 1976 |
| Description | (Point, closed subset)-separation axioms and closed subsets separation axioms for topological spaces will be uniformly defined. Then it is shown that a subcategory of TOP is bireflective in TOP if and only if Ob consists of all separated spaces for some (point, closed subset)-separation axiom. A characterization theorem on subcategories of all separated spaces for closed subsets separation axioms is also given by using the category SEP of all separation spaces and the embedding functor G: TOP → SEP. As an application we have that a $T_{1}$-space is normal if and only if it is embedded in a product space of the unit intervals in SEP. |
| Related Links | https://www.cambridge.org/core/services/aop-cambridge-core/content/view/79761DB7E20E377519E4D89DB96A2C22/S1446788700016347a.pdf/div-class-title-separation-axioms-and-subcategories-of-top-div.pdf |
| Ending Page | 490 |
| Page Count | 15 |
| Starting Page | 476 |
| ISSN | 14467887 |
| e-ISSN | 14468107 |
| DOI | 10.1017/s1446788700016347 |
| Journal | Journal of the Australian Mathematical Society |
| Issue Number | 4 |
| Volume Number | 22 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 1976-12-01 |
| Access Restriction | Open |
| Subject Keyword | Journal of the Australian Mathematical Society History and Philosophy of Science Subsets Separation Axioms |
| Content Type | Text |
| Resource Type | Article |
| Subject | Mathematics |
