Sum of Soft Topological Spaces
In this paper, we introduce the concept of sum of soft topological spaces using pairwise disjoint soft topological spaces and study its basic properties. Then, we define additive and finitely additive properties which are considered a link between soft topological spaces and their sum. In this regar...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-06-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/6/990 |
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| author | Tareq M. Al-shami Ljubiša D. R. Kočinac Baravan A. Asaad |
| author_facet | Tareq M. Al-shami Ljubiša D. R. Kočinac Baravan A. Asaad |
| author_sort | Tareq M. Al-shami |
| collection | DOAJ |
| description | In this paper, we introduce the concept of sum of soft topological spaces using pairwise disjoint soft topological spaces and study its basic properties. Then, we define additive and finitely additive properties which are considered a link between soft topological spaces and their sum. In this regard, we show that the properties of being p-soft <inline-formula> <math display="inline"> <semantics> <msub> <mi>T</mi> <mi>i</mi> </msub> </semantics> </math> </inline-formula>, soft paracompactness, soft extremally disconnectedness, and soft continuity are additive. We provide some examples to elucidate that soft compactness and soft separability are finitely additive; however, soft hyperconnected, soft indiscrete, and door soft spaces are not finitely additive. In addition, we prove that soft interior, soft closure, soft limit, and soft boundary points are interchangeable between soft topological spaces and their sum. This helps to obtain some results related to some important generalized soft open sets. Finally, we observe under which conditions a soft topological space represents the sum of some soft topological spaces. |
| first_indexed | 2024-03-10T19:06:42Z |
| format | Article |
| id | doaj.art-0aa8f97d25cc4b44aa51d0b125a705c7 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T19:06:42Z |
| publishDate | 2020-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-0aa8f97d25cc4b44aa51d0b125a705c72023-11-20T04:05:44ZengMDPI AGMathematics2227-73902020-06-018699010.3390/math8060990Sum of Soft Topological SpacesTareq M. Al-shami0Ljubiša D. R. Kočinac1Baravan A. Asaad2Department of Mathematics, Sana’a University, P.O.Box 1247 Sana’a, YemenFaculty of Sciences and Mathematics, University of Niš, 18000 Niš, SerbiaDepartment of Computer Science, College of Science, Cihan University-Duhok, Duhok 42001, IraqIn this paper, we introduce the concept of sum of soft topological spaces using pairwise disjoint soft topological spaces and study its basic properties. Then, we define additive and finitely additive properties which are considered a link between soft topological spaces and their sum. In this regard, we show that the properties of being p-soft <inline-formula> <math display="inline"> <semantics> <msub> <mi>T</mi> <mi>i</mi> </msub> </semantics> </math> </inline-formula>, soft paracompactness, soft extremally disconnectedness, and soft continuity are additive. We provide some examples to elucidate that soft compactness and soft separability are finitely additive; however, soft hyperconnected, soft indiscrete, and door soft spaces are not finitely additive. In addition, we prove that soft interior, soft closure, soft limit, and soft boundary points are interchangeable between soft topological spaces and their sum. This helps to obtain some results related to some important generalized soft open sets. Finally, we observe under which conditions a soft topological space represents the sum of some soft topological spaces.https://www.mdpi.com/2227-7390/8/6/990sum of soft topological spacesadditive propertyp-soft <i>Ti</i>soft compactnesssoft paracompactnesssoft extremally disconnectedness |
| spellingShingle | Tareq M. Al-shami Ljubiša D. R. Kočinac Baravan A. Asaad Sum of Soft Topological Spaces Mathematics sum of soft topological spaces additive property p-soft <i>Ti</i> soft compactness soft paracompactness soft extremally disconnectedness |
| title | Sum of Soft Topological Spaces |
| title_full | Sum of Soft Topological Spaces |
| title_fullStr | Sum of Soft Topological Spaces |
| title_full_unstemmed | Sum of Soft Topological Spaces |
| title_short | Sum of Soft Topological Spaces |
| title_sort | sum of soft topological spaces |
| topic | sum of soft topological spaces additive property p-soft <i>Ti</i> soft compactness soft paracompactness soft extremally disconnectedness |
| url | https://www.mdpi.com/2227-7390/8/6/990 |
| work_keys_str_mv | AT tareqmalshami sumofsofttopologicalspaces AT ljubisadrkocinac sumofsofttopologicalspaces AT baravanaasaad sumofsofttopologicalspaces |