Two New Versions of the Pasting Lemma via Soft Mixed Structure

Abstract

In this paper, we present two new generalizations of the pasting lemma using soft mixed structure. To do this, we introduce the notions of a $(\tau _{1},\tau _{2})$-$g$-closed soft set and a $(\tau _{1},\tau _{2})$-$gpr$% -closed soft set. We establish the notions of mixed $g$-soft continuity and mixed $gpr$-soft continuity between two soft topological spaces $(X,\tau _{1},\Delta _{1})$, $(X,\tau _{2},\Delta _{1})$ and a soft topological space $(X,\tau ,\Delta _{2})$. Finally we prove two new versions of the pasting lemma using the mixed $g$-soft continuous mapping and the mixed $gpr$-soft continuous mapping.