Structural Aspects of Weak Connectedness and Weak Compactness in Bipolar Soft Weak Structures

Connectedness and compactness are two essential properties that characterize the structural behavior of topological spaces. Extending these notions to bipolar soft topological spaces is crucial for analyzing systems involving both positive and negative information. In this paper, we define W ff-separated BP SSs and strong W ff-separated BP SSs using bipolar soft weak structures. We also introduce and investigate bipolar soft weak connectedness and bipolar soft weak compactness within bipolar soft weak structures. Furthermore, we define the concepts of bipolar soft weak local connectedness and bipolar soft weak components, supported by illustrative examples to clarify their meanings. Furthermore, we explore the relationships between these new concepts and their classical counterparts, showing that a BP S W ff-connected (resp. disconnected) space is not necessarily BP S W ff-hereditary, and that a BP SW-closed subset of a BP S W ff-compact space may fail to be BP S W ff-compact.