Three new soft separation axioms in soft topological spaces

Abstract

Soft $ \omega $-almost-regularity, soft $ \omega $ -semi-regularity, and soft $ \omega $-$ T_{2\frac{1}{2}} $ as three novel soft separation axioms are introduced. It is demonstrated that soft $ \omega $ -almost-regularity is strictly between "soft regularity" and "soft almost-regularity"; soft $ \omega $-$ T_{2\frac{1}{2}} $ is strictly between "soft $ T_{2\frac{1}{2}} $" and "soft $ T_{2} $", and soft $ \omega $ -semi-regularity is a weaker form of both "soft semi-regularity" and "soft $ \omega $-regularity". Several sufficient conditions for the equivalence between these new three notions and some of their relevant ones are given. Many characterizations of soft $ \omega $-almost-regularity are obtained, and a decomposition theorem of soft regularity by means of "soft $ \omega $ -semi-regularity" and "soft $ \omega $-almost-regularity" is obtained. Furthermore, it is shown that soft $ \omega $-almost-regularity is heritable for specific kinds of soft subspaces. It is also proved that the soft product of two soft $ \omega $-almost regular soft topological spaces is soft $ \omega $-almost regular. In addition, the connections between our three new conceptions and their topological counterpart topological spaces are discussed.

Keywords

• soft almost regularity
• soft $ \omega $ -openness
• soft $ r\omega $-openness
• soft regularity
• soft $ \omega $ -regularity
• soft semi-regularity