Sg-continuity in Topological Ordered Spaces

Abstract

Semi generalised closed set in a Topological space was first introduced by P. Bhattacharya and B.K.Lahiri in 1987. A subset A of a topological space (X,Ƭ) is a semi generalised closed (sg-closed) set if scl(A) ⊆ U whenever (A) ⊆ U and U is semi-open in (X,Ƭ) . Some authors introduced the notion of sg-continuity in topological spaces. The same notion can be extended to topological ordered spaces. A topological ordered space is a topological space together with a partial order. In this paper, we introduce and study the notion of semi generalised increasing continuous function (sgi-continuous function), semi generalised decreasing continuous function (sgd-continuous function) and semi generalised balanced continuous function (sgb-continuous function) and study the relationships between them.