Some Results of τ1τ2-δ Semiconnectedness and Compactness in Bitopological Spaces
We are going to establish some results of τ1τ2-δ semiconnectedness and compactness in a bitopological space. Besides, we will investigate several results in τ1τ2-δ semiconnectedness for subsets in bitopological spaces. In particular, we will discuss the relationship related to semiconnectedness betw...
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2018/7863713 |
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| author | M. Arunmaran K. Kannan |
| author_facet | M. Arunmaran K. Kannan |
| author_sort | M. Arunmaran |
| collection | DOAJ |
| description | We are going to establish some results of τ1τ2-δ semiconnectedness and compactness in a bitopological space. Besides, we will investigate several results in τ1τ2-δ semiconnectedness for subsets in bitopological spaces. In particular, we will discuss the relationship related to semiconnectedness between the topological spaces and bitopological space. That is, if a bitopological space (X,τ1,τ2) is τ1τ2-δ semiconnected, then the topological spaces (X,τ1) and (X,τ2) are δ-semiconnected. In addition, we introduce the result which states that a bitopological space (X,τ1,τ2) is τ1τ2-δ semiconnected if and only if X and ϕ are the only subsets of X which are τ1τ2-δ semiclopen sets. Moreover, we have proved some results in compactness also. Altogether, several results of τ1τ2-δ semiconnectedness and compactness in a bitopological space have been discussed. |
| format | Article |
| id | doaj-art-0a36a299b2084c3886429e14ff383fa8 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-0a36a299b2084c3886429e14ff383fa82025-02-03T01:09:30ZengWileyJournal of Mathematics2314-46292314-47852018-01-01201810.1155/2018/78637137863713Some Results of τ1τ2-δ Semiconnectedness and Compactness in Bitopological SpacesM. Arunmaran0K. Kannan1Department of Mathematics and Statistics, University of Jaffna, Jaffna, Sri LankaDepartment of Mathematics and Statistics, University of Jaffna, Jaffna, Sri LankaWe are going to establish some results of τ1τ2-δ semiconnectedness and compactness in a bitopological space. Besides, we will investigate several results in τ1τ2-δ semiconnectedness for subsets in bitopological spaces. In particular, we will discuss the relationship related to semiconnectedness between the topological spaces and bitopological space. That is, if a bitopological space (X,τ1,τ2) is τ1τ2-δ semiconnected, then the topological spaces (X,τ1) and (X,τ2) are δ-semiconnected. In addition, we introduce the result which states that a bitopological space (X,τ1,τ2) is τ1τ2-δ semiconnected if and only if X and ϕ are the only subsets of X which are τ1τ2-δ semiclopen sets. Moreover, we have proved some results in compactness also. Altogether, several results of τ1τ2-δ semiconnectedness and compactness in a bitopological space have been discussed.http://dx.doi.org/10.1155/2018/7863713 |
| spellingShingle | M. Arunmaran K. Kannan Some Results of τ1τ2-δ Semiconnectedness and Compactness in Bitopological Spaces Journal of Mathematics |
| title | Some Results of τ1τ2-δ Semiconnectedness and Compactness in Bitopological Spaces |
| title_full | Some Results of τ1τ2-δ Semiconnectedness and Compactness in Bitopological Spaces |
| title_fullStr | Some Results of τ1τ2-δ Semiconnectedness and Compactness in Bitopological Spaces |
| title_full_unstemmed | Some Results of τ1τ2-δ Semiconnectedness and Compactness in Bitopological Spaces |
| title_short | Some Results of τ1τ2-δ Semiconnectedness and Compactness in Bitopological Spaces |
| title_sort | some results of τ1τ2 δ semiconnectedness and compactness in bitopological spaces |
| url | http://dx.doi.org/10.1155/2018/7863713 |
| work_keys_str_mv | AT marunmaran someresultsoft1t2dsemiconnectednessandcompactnessinbitopologicalspaces AT kkannan someresultsoft1t2dsemiconnectednessandcompactnessinbitopologicalspaces |