Direct spectra of Bishop spaces and their limits
We apply fundamental notions of Bishop set theory (BST), an informal theory that complements Bishop's theory of sets, to the theory of Bishop spaces, a function-theoretic approach to constructive topology. Within BST we develop the notions of a direct family of sets, of a direct spectrum of Bis...
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| Format: | Article |
| Language: | English |
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Logical Methods in Computer Science e.V.
2021-04-01
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| Series: | Logical Methods in Computer Science |
| Subjects: | |
| Online Access: | https://lmcs.episciences.org/5615/pdf |
| _version_ | 1797268525710049280 |
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| author | Iosif Petrakis |
| author_facet | Iosif Petrakis |
| author_sort | Iosif Petrakis |
| collection | DOAJ |
| description | We apply fundamental notions of Bishop set theory (BST), an informal theory
that complements Bishop's theory of sets, to the theory of Bishop spaces, a
function-theoretic approach to constructive topology. Within BST we develop the
notions of a direct family of sets, of a direct spectrum of Bishop spaces, of
the direct limit of a direct spectrum of Bishop spaces, and of the inverse
limit of a contravariant direct spectrum of Bishop spaces. Within the extension
of Bishop's informal system of constructive mathematics BISH with inductive
definitions with rules of countably many premises, we prove the fundamental
theorems on the direct and inverse limits of spectra of Bishop spaces and the
duality principle between them. |
| first_indexed | 2024-04-25T01:33:52Z |
| format | Article |
| id | doaj.art-d9abd598721e4c96a6a94356fcd5392e |
| institution | Directory Open Access Journal |
| issn | 1860-5974 |
| language | English |
| last_indexed | 2024-04-25T01:33:52Z |
| publishDate | 2021-04-01 |
| publisher | Logical Methods in Computer Science e.V. |
| record_format | Article |
| series | Logical Methods in Computer Science |
| spelling | doaj.art-d9abd598721e4c96a6a94356fcd5392e2024-03-08T10:33:57ZengLogical Methods in Computer Science e.V.Logical Methods in Computer Science1860-59742021-04-01Volume 17, Issue 210.23638/LMCS-17(2:4)20215615Direct spectra of Bishop spaces and their limitsIosif PetrakisWe apply fundamental notions of Bishop set theory (BST), an informal theory that complements Bishop's theory of sets, to the theory of Bishop spaces, a function-theoretic approach to constructive topology. Within BST we develop the notions of a direct family of sets, of a direct spectrum of Bishop spaces, of the direct limit of a direct spectrum of Bishop spaces, and of the inverse limit of a contravariant direct spectrum of Bishop spaces. Within the extension of Bishop's informal system of constructive mathematics BISH with inductive definitions with rules of countably many premises, we prove the fundamental theorems on the direct and inverse limits of spectra of Bishop spaces and the duality principle between them.https://lmcs.episciences.org/5615/pdfmathematics - logic |
| spellingShingle | Iosif Petrakis Direct spectra of Bishop spaces and their limits Logical Methods in Computer Science mathematics - logic |
| title | Direct spectra of Bishop spaces and their limits |
| title_full | Direct spectra of Bishop spaces and their limits |
| title_fullStr | Direct spectra of Bishop spaces and their limits |
| title_full_unstemmed | Direct spectra of Bishop spaces and their limits |
| title_short | Direct spectra of Bishop spaces and their limits |
| title_sort | direct spectra of bishop spaces and their limits |
| topic | mathematics - logic |
| url | https://lmcs.episciences.org/5615/pdf |
| work_keys_str_mv | AT iosifpetrakis directspectraofbishopspacesandtheirlimits |