On soft p-regularity and soft almost-p-regularity

This paper introduces two new weak forms of soft regularity in soft topology: soft $p$-regular and soft almost- $p$-regular. These forms extend their analogous notions in classical topological spaces by incorporating soft sets, providing a flexible framework for dealing with uncertainty or imprecision. We obtain several characterizations of each of them and investigate the correspondences between them and their analogous concepts in classical topological spaces. Also, we prove that soft $p$ -regularity lies strictly between soft regularity and soft almost- $p$ -regularity. Moreover, we show that soft $p$-regularity (resp. soft almost $p$-regularity) is preserved under soft $\alpha$-open subspaces (resp. soft regular-open subspaces). In addition, we prove that soft $p$-regularity and soft almost $p$-regularity are soft productive. Finally, we obtain some preservation theorems regarding soft $p$-regularity and soft almost- $p$-regularity.