Soft Faint Continuity and Soft Faint Theta Omega Continuity between Soft Topological Spaces

Abstract

The concepts of soft faint continuity as a weaker form of soft weak continuity and soft faint θω-continuity as a weaker form of soft weak θω-continuity are introduced. Numerous characterizations of them are given. We further demonstrate that, under soft restrictions, they are retained. Moreover, we show that a soft function is soft faintly continuous (respectively, soft faintly θω-continuous) if its soft graph function is soft faintly continuous (respectively, soft faintly θω-continuous). In addition, we show that a soft function with a soft almost regular (respectively, soft extremally disconnected) co-domain is soft faintly continuous iff it is soft almost continuous (respectively, soft δ-continuous). Furthermore, we show that soft faintly continuous surjective functions are soft set-connected functions, and as a corollary, we demonstrate how soft faintly continuous functions sustain soft connectivity. Finally, we studied the symmetry between our new notions and their topological counterparts.

Keywords

• soft <i>θ</i>-openness
• soft <i>θ_ω</i>-openness
• soft connectedness
• faint continuity
• generated soft topology