On Soft Pre-α-Open Sets and Soft Pre-α-continuous Functions in Soft Topological Spaces

Abstract

In this paper, we introduce a new class of generalized soft open sets in soft
topological spaces, namely, soft pre-α-open sets and we show that the
family of all soft pre-α-open subsets of a soft topological space
,E)
~ (X, 
form a soft topology on X which is soft finer than

~
. Soft pre-α-open sets
is stronger than each of soft semi-open sets, soft α-open sets, soft pre-open
sets, soft b-open sets, soft β-open sets, soft generalized semi open sets, soft
generalized α-open sets and soft α-generalized open sets and weaker than
soft open sets. Moreover, we use these soft sets to define and study new
classes of soft functions, namely, soft pre-α-continuous functions and soft
pre-α-irresolute functions in soft topological spaces and we discuss the
relation between these soft functions and each of soft continuous functions
and other weaker forms of soft continuous functions.