MAPPINGS AND DECOMPOSITIONS OF (μ, σ)-CONTINUITY ON μ-NEARLY COMPACT SPACES

Abstract

In generalised topological space (X,μ), a μ-space is said to be μ-nearly compact if every μ-regular open cover of X has a finite subcover. In literature, many generalised continuities in a topological space are constructed using many generalised open sets. Relationships among them are studied by proving their implications and finding counterexamples for their independent relationships. Many researchers called this type of study a decomposition of continuities. In this paper, we further investigate some decompositions of (μ,σ)-continuity and applying them to μ-nearly compact spaces. Moreover, we also analyse the effect of mappings on these spaces and obtain some results. The main result is that the (μ,σ)-δ-continuous image of μ-nearly compact space is σ-nearly compact.