On soft covering spaces in soft topological spaces

Mohammed Abu Saleem; Mohammed Abu Saleem

doi:10.3934/math.2024885

AIMS Mathematics

2024, Volume 9, Issue 7: 18134-18142. doi: 10.3934/math.2024885

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Research article

On soft covering spaces in soft topological spaces

Mohammed Abu Saleem ^,

Department of Mathematics, Faculty of Science, Al-Balqa Applied University, Salt 19117, Jordan

Received: 16 March 2024 Revised: 10 May 2024 Accepted: 16 May 2024 Published: 29 May 2024
MSC : 7M10, 57M12, 54-XX, 54A40

In this paper, we present the concept of a soft covering map on a soft topological space. We also introduce the notion of a soft local homeomorphism and establish the relationship between soft local homeomorphism and soft open mapping. Additionally, we demonstrate that a soft local homeomorphism does not necessarily imply a soft covering map. We provide several characterizations and restriction theorems. Moreover, we deduce the necessary and sufficient conditions for a soft continuous map to be a soft covering map.
- soft covering map,
- soft covering space,
- soft local homeomorphism
Citation: Mohammed Abu Saleem. On soft covering spaces in soft topological spaces[J]. AIMS Mathematics, 2024, 9(7): 18134-18142. doi: 10.3934/math.2024885

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Abstract

In this paper, we present the concept of a soft covering map on a soft topological space. We also introduce the notion of a soft local homeomorphism and establish the relationship between soft local homeomorphism and soft open mapping. Additionally, we demonstrate that a soft local homeomorphism does not necessarily imply a soft covering map. We provide several characterizations and restriction theorems. Moreover, we deduce the necessary and sufficient conditions for a soft continuous map to be a soft covering map.

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