Functorial comparisons of bitopology with topology and the case for redundancy of bitopology in lattice-valued mathematics
This paper studies various functors between (lattice-valued) topology and (lattice-valued) bitopology, including the expected “doubling” functor Ed : L-Top → L-BiTop and the “cross” functor E× : L-BiTop → L2-Top introduced in this paper, both of which are extremely well-behaved strict, concrete, ful...
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| Format: | Article |
| Language: | English |
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Universitat Politècnica de València
2008-04-01
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| Series: | Applied General Topology |
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| Online Access: | http://polipapers.upv.es/index.php/AGT/article/view/1871 |
| _version_ | 1811279640318181376 |
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| author | S.E. Rodabaugh |
| author_facet | S.E. Rodabaugh |
| author_sort | S.E. Rodabaugh |
| collection | DOAJ |
| description | This paper studies various functors between (lattice-valued) topology and (lattice-valued) bitopology, including the expected “doubling” functor Ed : L-Top → L-BiTop and the “cross” functor E× : L-BiTop → L2-Top introduced in this paper, both of which are extremely well-behaved strict, concrete, full embeddings. Given the greater simplicity of lattice-valued topology vis-a-vis lattice-valued bitopology and the fact that the class of L2-Top’s is strictly smaller than the class of L-Top’s encompassing fixed-basis topology, the class of E×’s makes the case that lattice-valued bitopology is categorically redundant. As a special application, traditional bitopology as represented by BiTop is (isomorphic in an extremely well-behaved way to) a strict subcategory of 4-Top, where 4 is the four element Boolean algebra; this makes the case that traditional bitopology is a special case of a much simpler fixed-basis topology. |
| first_indexed | 2024-04-13T00:59:19Z |
| format | Article |
| id | doaj.art-fdef3f907e5f4b54887c0ce8e059d066 |
| institution | Directory Open Access Journal |
| issn | 1576-9402 1989-4147 |
| language | English |
| last_indexed | 2024-04-13T00:59:19Z |
| publishDate | 2008-04-01 |
| publisher | Universitat Politècnica de València |
| record_format | Article |
| series | Applied General Topology |
| spelling | doaj.art-fdef3f907e5f4b54887c0ce8e059d0662022-12-22T03:09:33ZengUniversitat Politècnica de ValènciaApplied General Topology1576-94021989-41472008-04-01917710810.4995/agt.2008.18711515Functorial comparisons of bitopology with topology and the case for redundancy of bitopology in lattice-valued mathematicsS.E. Rodabaugh0Youngstown State UniversityThis paper studies various functors between (lattice-valued) topology and (lattice-valued) bitopology, including the expected “doubling” functor Ed : L-Top → L-BiTop and the “cross” functor E× : L-BiTop → L2-Top introduced in this paper, both of which are extremely well-behaved strict, concrete, full embeddings. Given the greater simplicity of lattice-valued topology vis-a-vis lattice-valued bitopology and the fact that the class of L2-Top’s is strictly smaller than the class of L-Top’s encompassing fixed-basis topology, the class of E×’s makes the case that lattice-valued bitopology is categorically redundant. As a special application, traditional bitopology as represented by BiTop is (isomorphic in an extremely well-behaved way to) a strict subcategory of 4-Top, where 4 is the four element Boolean algebra; this makes the case that traditional bitopology is a special case of a much simpler fixed-basis topology.http://polipapers.upv.es/index.php/AGT/article/view/1871Unital-semi-quantaleUnital quantale(fixed-basis) topology(fixed-basis) bitopologyOrder-isomorphismCategorical (functorial) embeddingRedundancy |
| spellingShingle | S.E. Rodabaugh Functorial comparisons of bitopology with topology and the case for redundancy of bitopology in lattice-valued mathematics Applied General Topology Unital-semi-quantale Unital quantale (fixed-basis) topology (fixed-basis) bitopology Order-isomorphism Categorical (functorial) embedding Redundancy |
| title | Functorial comparisons of bitopology with topology and the case for redundancy of bitopology in lattice-valued mathematics |
| title_full | Functorial comparisons of bitopology with topology and the case for redundancy of bitopology in lattice-valued mathematics |
| title_fullStr | Functorial comparisons of bitopology with topology and the case for redundancy of bitopology in lattice-valued mathematics |
| title_full_unstemmed | Functorial comparisons of bitopology with topology and the case for redundancy of bitopology in lattice-valued mathematics |
| title_short | Functorial comparisons of bitopology with topology and the case for redundancy of bitopology in lattice-valued mathematics |
| title_sort | functorial comparisons of bitopology with topology and the case for redundancy of bitopology in lattice valued mathematics |
| topic | Unital-semi-quantale Unital quantale (fixed-basis) topology (fixed-basis) bitopology Order-isomorphism Categorical (functorial) embedding Redundancy |
| url | http://polipapers.upv.es/index.php/AGT/article/view/1871 |
| work_keys_str_mv | AT serodabaugh functorialcomparisonsofbitopologywithtopologyandthecaseforredundancyofbitopologyinlatticevaluedmathematics |