Bipolar Soft Minimal Structures

Abstract

The purpose of this paper is to introduce a new structure of bipolar soft topology called bipolar soft minimal structure. Later, we present most important operators in bipolar soft minimal spaces such as $\widetilde{\widetilde{\mathfrak{m}}}$-interior, $ \widetilde{\widetilde{\mathfrak{m}}} $-closure and $ \widetilde{\widetilde{\mathfrak{m}}} $-boundary. Moreover, we define $ \widetilde{\widetilde{\mathfrak{m}}} $-separated bipolar soft sets and bipolar soft $ \widetilde{\widetilde{\mathfrak{m}}} $-connected sets. Furthermore, we introduce a new concept of bipolar soft minimal spaces called bipolar soft minimal connected. We prove that the bipolar soft intersection of a pair of bipolar soft $ \widetilde{\widetilde{\mathfrak{m}}} $-connected spaces over the common universal set is a bipolar soft $ \widetilde{\widetilde{\mathfrak{m}}} $-connected space. In addition, we show that bipolar soft $ \widetilde{\widetilde{\mathfrak{m}}} $-connected space is not a bipolar soft $ \widetilde{\widetilde{\mathfrak{m}}} $-hereditary property. Also, we discuss some relations, properties and results of these new concepts of bipolar soft minimal spaces. Finally, some counterexamples are provided.