# $$\alpha_\beta$$-Connectedness as a characterization of connectedness

## Abstract

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.

## Article Details

How to Cite
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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