Degrees of <i>L</i>-Continuity for Mappings between <i>L</i>-Topological Spaces
By means of the residual implication on a frame <i>L</i>, a degree approach to <i>L</i>-continuity and <i>L</i>-closedness for mappings between <i>L</i>-cotopological spaces are defined and their properties are investigated systematically. In addition,...
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MDPI AG
2019-10-01
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| Online Access: | https://www.mdpi.com/2227-7390/7/11/1013 |
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| author | Zhenyu Xiu Qinghua Li |
| author_facet | Zhenyu Xiu Qinghua Li |
| author_sort | Zhenyu Xiu |
| collection | DOAJ |
| description | By means of the residual implication on a frame <i>L</i>, a degree approach to <i>L</i>-continuity and <i>L</i>-closedness for mappings between <i>L</i>-cotopological spaces are defined and their properties are investigated systematically. In addition, in the situation of <i>L</i>-topological spaces, degrees of <i>L</i>-continuity and of <i>L</i>-openness for mappings are proposed and their connections are studied. Moreover, if <i>L</i> is a frame with an order-reversing involution <inline-formula> <math display="inline"> <semantics> <msup> <mrow></mrow> <mo>′</mo> </msup> </semantics> </math> </inline-formula>, where <inline-formula> <math display="inline"> <semantics> <mrow> <msup> <mi>b</mi> <mo>′</mo> </msup> <mo>=</mo> <mi>b</mi> <mo>→</mo> <mo>⟂</mo> </mrow> </semantics> </math> </inline-formula> for <inline-formula> <math display="inline"> <semantics> <mrow> <mi>b</mi> <mo>∈</mo> <mi>L</mi> </mrow> </semantics> </math> </inline-formula>, then degrees of <i>L</i>-continuity for mappings between <i>L</i>-cotopological spaces and degrees of <i>L</i>-continuity for mappings between <i>L</i>-topological spaces are equivalent. |
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| last_indexed | 2024-12-11T20:24:18Z |
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| spelling | doaj.art-815662bf372a42b980a9c0635accfcce2022-12-22T00:51:59ZengMDPI AGMathematics2227-73902019-10-01711101310.3390/math7111013math7111013Degrees of <i>L</i>-Continuity for Mappings between <i>L</i>-Topological SpacesZhenyu Xiu0Qinghua Li1College of Applied Mathematics, Chengdu University of Information Technology, Chengdu 610000, ChinaSchool of Mathematics and Information Sciences, Yantai University, Yantai 264005, ChinaBy means of the residual implication on a frame <i>L</i>, a degree approach to <i>L</i>-continuity and <i>L</i>-closedness for mappings between <i>L</i>-cotopological spaces are defined and their properties are investigated systematically. In addition, in the situation of <i>L</i>-topological spaces, degrees of <i>L</i>-continuity and of <i>L</i>-openness for mappings are proposed and their connections are studied. Moreover, if <i>L</i> is a frame with an order-reversing involution <inline-formula> <math display="inline"> <semantics> <msup> <mrow></mrow> <mo>′</mo> </msup> </semantics> </math> </inline-formula>, where <inline-formula> <math display="inline"> <semantics> <mrow> <msup> <mi>b</mi> <mo>′</mo> </msup> <mo>=</mo> <mi>b</mi> <mo>→</mo> <mo>⟂</mo> </mrow> </semantics> </math> </inline-formula> for <inline-formula> <math display="inline"> <semantics> <mrow> <mi>b</mi> <mo>∈</mo> <mi>L</mi> </mrow> </semantics> </math> </inline-formula>, then degrees of <i>L</i>-continuity for mappings between <i>L</i>-cotopological spaces and degrees of <i>L</i>-continuity for mappings between <i>L</i>-topological spaces are equivalent.https://www.mdpi.com/2227-7390/7/11/1013<i>l</i>-cotopological space<i>l</i>-topological spacedegree of <i>l</i>-continuitydegree of <i>l</i>-closednessdegree of <i>l</i>-openness |
| spellingShingle | Zhenyu Xiu Qinghua Li Degrees of <i>L</i>-Continuity for Mappings between <i>L</i>-Topological Spaces Mathematics <i>l</i>-cotopological space <i>l</i>-topological space degree of <i>l</i>-continuity degree of <i>l</i>-closedness degree of <i>l</i>-openness |
| title | Degrees of <i>L</i>-Continuity for Mappings between <i>L</i>-Topological Spaces |
| title_full | Degrees of <i>L</i>-Continuity for Mappings between <i>L</i>-Topological Spaces |
| title_fullStr | Degrees of <i>L</i>-Continuity for Mappings between <i>L</i>-Topological Spaces |
| title_full_unstemmed | Degrees of <i>L</i>-Continuity for Mappings between <i>L</i>-Topological Spaces |
| title_short | Degrees of <i>L</i>-Continuity for Mappings between <i>L</i>-Topological Spaces |
| title_sort | degrees of i l i continuity for mappings between i l i topological spaces |
| topic | <i>l</i>-cotopological space <i>l</i>-topological space degree of <i>l</i>-continuity degree of <i>l</i>-closedness degree of <i>l</i>-openness |
| url | https://www.mdpi.com/2227-7390/7/11/1013 |
| work_keys_str_mv | AT zhenyuxiu degreesofilicontinuityformappingsbetweenilitopologicalspaces AT qinghuali degreesofilicontinuityformappingsbetweenilitopologicalspaces |