A note on closure spaces determined by intersections
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| Title: | A note on closure spaces determined by intersections |
|---|---|
| Authors: | Víctor Fernández, Cristian Brunetta |
| Source: | Boletim da Sociedade Paranaense de Matemática, Vol 41 (2022) |
| Publisher Information: | Sociedade Paranaense de Matemática, 2022. |
| Publication Year: | 2022 |
| Subject Terms: | Rough Sets Theory and Applications, FOS: Political science, Generalization, Set (abstract data type), FOS: Law, Mathematical analysis, Description Logics, 12. Responsible consumption, Logic Programming and Knowledge Representation, Artificial Intelligence, Fuzzy Logic and Residuated Lattices, 11. Sustainability, QA1-939, FOS: Mathematics, Political science, Linear subspace, Physics, Pure mathematics, Optics, Discrete mathematics, Focus (optics), 16. Peace & justice, Computer science, Programming language, Computational Theory and Mathematics, Computer Science, Physical Sciences, Closure (psychology), Law, Mathematics |
| Description: | In this work, we study a kind of closure systems (c.s.) that are defined by means of intersections of subsets of a support X with a (fixed) closed set T. These systems (which will be indicated by M(T)-spaces) can be understood as a generalization of the usual relative subspaces. Several results (referred to continuity and to the ordered structure of families of M(T)-spaces) are shown here. In addition, we study the transference of properties from the ``original closure spaces (X,K) to the spaces (X,M(T)). Among them, we are interested mainly in finitariness and in structurality. In this study of transference, we focus our analyisis on the c.s. usually known as abstract logics, and we show some results for them. |
| Document Type: | Article Other literature type |
| ISSN: | 2175-1188 0037-8712 |
| DOI: | 10.5269/bspm.52790 |
| DOI: | 10.60692/2t4w6-g3b50 |
| DOI: | 10.60692/fcnvy-d8x32 |
| Access URL: | https://doaj.org/article/9a58f33ceec4455da5a914ed168b414a |
| Rights: | CC BY |
| Accession Number: | edsair.doi.dedup.....1f36490618f30eb8445df6e4af984ad0 |
| Database: | OpenAIRE |
Nájsť tento článok vo Web of Science | Abstract: | In this work, we study a kind of closure systems (c.s.) that are defined by means of intersections of subsets of a support X with a (fixed) closed set T. These systems (which will be indicated by M(T)-spaces) can be understood as a generalization of the usual relative subspaces. Several results (referred to continuity and to the ordered structure of families of M(T)-spaces) are shown here. In addition, we study the transference of properties from the ``original closure spaces (X,K) to the spaces (X,M(T)). Among them, we are interested mainly in finitariness and in structurality. In this study of transference, we focus our analyisis on the c.s. usually known as abstract logics, and we show some results for them. |
|---|---|
| ISSN: | 21751188 00378712 |
| DOI: | 10.5269/bspm.52790 |