The Concept of Sg-continuity in Topological Ordered Spaces

In a topological space, the semi generalized closed set was initially developed by P. Bhattacharya and B.K. Lahiri in [1]. A subset of a topological space (X, \(\tau\)) is a semi generalised closed (sg-closed) set if scl(A) \(\subseteq\) U whenever A \(\subseteq\) U and U is semi-open in (X, \(\tau\)). The notion of sg-continuity was introduced by several authors in topological spaces. The same notion can also be extended to topological ordered spaces. A topological ordered space is a topological space together with a partial order. In the present chapter, the notion of semi-generalized increasing continuous function (sgi-continuous function), semi-generalized decreasing continuous function (sgd-continuous function), and semi-generalized balanced continuous function (sgb-continuous function) are introduced and their relationship with other functions are examined.