Map gluing theorems for theta-continuous and s \(\theta\)-continuous maps on topological spaces

Abstract

We obtain map gluing theorems on \(\theta\)-continuity and s\(\theta\)-continuity of maps on topological spaces, in terms of corresponding conditions on the restriction maps to certain subsets of the domain space. Sets containing all the points of s \(\theta\) discontinuities and \(\theta\)-discontinuities are obtained. Examples are given to illustrate the necessities of the conditions imposed on the restriction maps.