\(\alpha_\beta\)-Connectedness as a characterization of connectedness

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B. K. Tyagi
Manoj Bhardwaj
Sumit Singh


In this paper, a new class of \(\alpha_\beta\)-open sets in a topological space \(X\) is introduced which forms a topology on \(X\). The connectedness of this new topology on \(X\), called \(\alpha_\beta\)-connectedness, turns out to be equivalent to connectedness of \(X\) and hence also to \(\alpha\)-connectedness of \(X\). The \(\alpha_\beta\)-continuous and \(\alpha_\beta\)-irresolute mappings are defined and their relationship with other mappings such as continuous mappings and \(\alpha\)-continuous mappings are discussed. An intermediate value theorem is obtained. The hyperconnected spaces constitute a subclass of \(\alpha_\beta\)-connected spaces.

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Tyagi, B. K., Bhardwaj, M., & Singh, S. (2018). \(\alpha_\beta\)-Connectedness as a characterization of connectedness. Journal of Advanced Studies in Topology, 9(2), 119-129. https://doi.org/10.20454/jast.2018.1401
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