$L$-Topological Spaces
By substituting the usual notion of open sets in a topological space $X$ with a suitable collection of maps from $X$ to a frame $L$, we introduce the notion of L-topological spaces. Then, we proceed to study the classical notions and properties of usual topological spaces to the newly defined mathe...
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| Format: | Article |
| Language: | English |
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University of Maragheh
2018-04-01
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| Series: | Sahand Communications in Mathematical Analysis |
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| Online Access: | http://scma.maragheh.ac.ir/article_28387_de42aeb44cc0345bcda542f42caad0ac.pdf |
| _version_ | 1819046967204904960 |
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| author | Ali Bajravani |
| author_facet | Ali Bajravani |
| author_sort | Ali Bajravani |
| collection | DOAJ |
| description | By substituting the usual notion of open sets in a topological space $X$ with a suitable collection of maps from $X$ to a frame $L$, we introduce the notion of L-topological spaces. Then, we proceed to study the classical notions and properties of usual topological spaces to the newly defined mathematical notion. Our emphasis would be concentrated on the well understood classical connectedness, quotient and compactness notions, where we prove the Thychonoff's theorem and connectedness property for ultra product of $L$-compact and $L$-connected topological spaces, respectively. |
| first_indexed | 2024-12-21T10:52:52Z |
| format | Article |
| id | doaj.art-770c280d867848f6b78e1bdf7f970e25 |
| institution | Directory Open Access Journal |
| issn | 2322-5807 2423-3900 |
| language | English |
| last_indexed | 2024-12-21T10:52:52Z |
| publishDate | 2018-04-01 |
| publisher | University of Maragheh |
| record_format | Article |
| series | Sahand Communications in Mathematical Analysis |
| spelling | doaj.art-770c280d867848f6b78e1bdf7f970e252022-12-21T19:06:37ZengUniversity of MaraghehSahand Communications in Mathematical Analysis2322-58072423-39002018-04-0110111913310.22130/scma.2017.2838728387$L$-Topological SpacesAli Bajravani0Department of Mathematics, Faculty of Basic Sciences, Azarbaijan Shahid Madani University, Tabriz, I. R. Iran.By substituting the usual notion of open sets in a topological space $X$ with a suitable collection of maps from $X$ to a frame $L$, we introduce the notion of L-topological spaces. Then, we proceed to study the classical notions and properties of usual topological spaces to the newly defined mathematical notion. Our emphasis would be concentrated on the well understood classical connectedness, quotient and compactness notions, where we prove the Thychonoff's theorem and connectedness property for ultra product of $L$-compact and $L$-connected topological spaces, respectively.http://scma.maragheh.ac.ir/article_28387_de42aeb44cc0345bcda542f42caad0ac.pdfCompact SpacesConnected SpacesFrame |
| spellingShingle | Ali Bajravani $L$-Topological Spaces Sahand Communications in Mathematical Analysis Compact Spaces Connected Spaces Frame |
| title | $L$-Topological Spaces |
| title_full | $L$-Topological Spaces |
| title_fullStr | $L$-Topological Spaces |
| title_full_unstemmed | $L$-Topological Spaces |
| title_short | $L$-Topological Spaces |
| title_sort | l topological spaces |
| topic | Compact Spaces Connected Spaces Frame |
| url | http://scma.maragheh.ac.ir/article_28387_de42aeb44cc0345bcda542f42caad0ac.pdf |
| work_keys_str_mv | AT alibajravani ltopologicalspaces |