Three Weaker Forms of Soft Faint Continuity

Abstract

The authors of this paper introduce and discuss three weaker forms of soft faint continuity: soft faint semi-continuity, soft faint pre-continuity, and soft faint β-continuity. They characterize each of them in several ways. They also demonstrate how they are preserved under some restrictions. Moreover, they prove that a soft function is also soft faint semi-continuous (resp. soft faint pre-continuous, soft faint β-continuous) if its soft graph function is also soft faint semi-continuous (resp. soft faint pre-continuous, soft faint β-continuous). Moreover, they show that a soft function is soft faint semi-continuous (resp. soft faint pre-continuous, soft faint β-continuous) iff it is soft semi-continuous provided that it has a soft regular codomain. Finally, the symmetry between our new ideas and their analogous topological ones is investigated.

Keywords

• soft semi-openness
• soft pre-openness
• soft <i>β</i>-openness
• soft faint continuity
• generated soft topology