$ S $-$ \delta $-connectedness in $ S $-proximity spaces

Year 2021, Volume: 70 Issue: 2, 600 - 611, 31.12.2021

Beenu Singh , Davinder Singh

https://doi.org/10.31801/cfsuasmas.792265

Cited By: 2

https://izlik.org/JA74NT66CT

Abstract

New types of connectedness in $ S $-proximity spaces, named as an $ S $-$\delta$-connectedness, local $ S $-$ \delta $-connectedness are introduced. Also, their inter-relationships are studied. In an $ S $-proximity space $ (X, \delta_{X}) $, the $ S $-$ \delta $-connectedness of a subset $ U $ of $ X $ with respect to $ \delta_{X} $ may not be same as the $ S $-$ \delta $-connectedness of $ U $ with respect to its subspace proximity $ \delta_{U} $. Further, $ S $-$ \delta $-component and $ S $-$ \delta $-treelike spaces are also defined and a number of results are given.

Keywords

$ S $-proximity space , $\delta$-Connected , $ \delta $-component , locally $\delta$-Connected , $ \delta $-treelike

Supporting Institution

University Grants Commission, India

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