Three new soft separation axioms in soft topological spaces

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.