This paper introduces a novel concept of supra-soft topology generated from a specific family of supra-topologies. We define supra-soft $\omega$-open sets as a new class of soft sets that create a finer topology than the original. We explore the properties of these supra-soft $\omega$-open sets and assess the validity of related results from ordinary supra-topological spaces within the framework of supra-soft topological spaces. Additionally, we present two new separation axioms: supra-soft $\omega$-local indiscreteness and supra-soft $\omega$ -regularity, demonstrating that both are stronger than traditional supra-soft $\omega$-regularity. We also provide subspace and product theorems for supra-soft $\omega$-regularity and examine the correspondence between our new supra-soft concepts and their classical counterparts in supra-topology.

Beyond the realm of soft topology, soft continuity can aid in the creation of digital images and computational topological applications. This paper investigates soft almost weakly continuous, a novel family of generalized soft continuous functions. The soft pre-continuous and soft weakly continuous function classes are included in this class. We obtain many characterizations of soft almost weakly continuous functions. Furthermore, we investigate the link between soft almost weakly continuous functions and their general topology counterparts. We present adequate conditions for a soft almost weakly continuous function to become soft weakly continuous (soft pre-continuous). We also present various results of soft composition, restriction, preservation, product, and soft graph theorems in terms of soft almost weakly continuous functions.

We continued the study of "soft strong $\theta$-continuity" and defined and investigated "soft almost strong $\theta$-continuity" which is a generalization of soft strong $\theta$-continuity. We gave characterizations and examined soft composition concerning these two concepts. Furthermore, we derived several soft mapping theorems. We provided several links between these two ideas and their related concepts through examples. Lastly, we looked at the symmetry between them and their topological counterparts.

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.

Firstly, for the topological spaces that contain a minimal open set, we obtain various inclusions between minimal open sets and homogeneity components. For a given soft topological space $(X,\tau ,A)$, we define soft homogeneous components. We show that soft homogeneous components of $(X,\tau ,A)$ form a soft partition of the absolute soft set. Also, we show that $(X,\tau ,A)$ is soft homogeneous if and only if it has only one soft homogeneous component. Moreover, we study the relationships between the soft homogeneous components of $(X,\tau ,A)$ and the homogeneous component. For the soft topological spaces that contain a minimal soft open set, we obtain various inclusions between minimal soft open sets and soft homogeneity components. In addition, we show that soft homeomorphisms stabilize soft homogeneous components. Additionally, we introduce two soft product theorems concerning soft homogeneity and soft minimality, respectively.