Soft maps via soft somewhere dense sets in its different aspects

Abstract

Molodtsov [24] presented the concept of soft sets which are consider as an effective method to deal with vagueness and then, the development of soft sets gradually increased. In this paper, we introduce the concepts of soft SD-continuous, soft SD-open, soft SD-closed and
soft SD-homeomorphism maps whose definitions mainly depend on the soft somewhere dense and soft cs-dense sets. In these definitions, we discuss some logical expectations and additions which help to preserve some symmetric relations. We characterize these concepts and give some
interesting examples to show some obtained results. Furthermore, we investigate the role of soft hyperconnectedness concept to obtain some results related to graph and restriction of soft maps.