Pβ-connectedness in topological spaces
A new property called Pβ-connectedness is introduced which is stronger than connectedness and equivalent to pre-connectedness. The properties of this notion are explored and its relationship with other forms of connectedness, for example hyperconnectedness etc. are discussed. Locally pre-indiscrete...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2017-12-01
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| Series: | Demonstratio Mathematica |
| Subjects: | |
| Online Access: | http://www.degruyter.com/view/j/dema.2017.50.issue-1/dema-2017-0031/dema-2017-0031.xml?format=INT |
| Summary: | A new property called Pβ-connectedness is introduced which is stronger than connectedness and equivalent to pre-connectedness. The properties of this notion are explored and its relationship with other forms of connectedness, for example hyperconnectedness etc. are discussed. Locally pre-indiscrete spaces are defined as the spaces in which pre-open sets are closed. In such spaces connectedness becomes equivalent to pre-connectedness and hence to Pβ-connectedness, and semi-connectedness becomes equivalent to Pβ- connectedness. The notion of locally Pβ-connected space is introduced. The behavior of Pβ-connectedness under several types of mappings is investigated. An intermediate value theorem is obtained. |
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| ISSN: | 2391-4661 |