Pβ-connectedness in topological spaces

• Main Authors: Tyagi Brij K., Singh Sumit, Bhardwaj Manoj
• Format: Article
• Language: English
• Published: De Gruyter 2017-12-01
• Series: Demonstratio Mathematica
• Subjects: pre-connected; β-connected; Pβ-continous mappings; Pβ-connected; topological spaces
• Online Access: http://www.degruyter.com/view/j/dema.2017.50.issue-1/dema-2017-0031/dema-2017-0031.xml?format=INT

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.