Topological Structures via Bipolar Hypersoft Sets
Sagvan Y. Musa ¡ Baravan A. Asaad
āĻāĻžāĻ¨ā§ ā§¨ā§Ļā§¨ā§Š ¡ HyperSoft Set āĻāĻŋāĻ¤āĻžāĻĒ 37 ¡ Infinite Study
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In this article, we introduce bipolar hypersoft topological spaces over the collection of bipolar hypersoft sets. It is proven that a bipolar hypersoft topological space gives a parametrized family of hypersoft topological spaces, but the converse does not hold in general, and this is shown with the help of an example. Furthermore, we give a condition on a given parametrized family of hypersoft topologies, which assure that there is a bipolar hypersoft topology whose induced family of hypersoft topologies is the given family. The notions of bipolar hypersoft neighborhood, bipolar hypersoft subspace, and bipolar hypersoft limit points are introduced. Finally, we define bipolar hypersoft interior, bipolar hypersoft closure, bipolar hypersoft exterior, and bipolar hypersoft boundary, and the relations between them, differing from the relations on hypersoft topology, are investigated.
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