Topological Structures Via Bipolar Hypersoft Sets
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Topological Structures via Bipolar Hypersoft Sets
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.
Connectedness on Hypersoft Topological Spaces
Connectedness (resp. disconnectedness), which reflects the key characteristic of topological spaces and helps in the differentiation of two topologies, is one of the most significant and fundamental concept in topological spaces. In light of this, we introduce hypersoft connectedness (resp. hypersoft disconnectedness) in hypersoft topological spaces and investigate its properties in details.
Neutrosophic Sets and Systems, vol. 55/2023
Author: Florentin Smarandache
language: en
Publisher: Infinite Study
Release Date: 2024-02-15
“Neutrosophic Sets and Systems” has been created for publications on advanced studies in neutrosophy, neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc. Neutrosophy is a new branch of philosophy that studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. This theory considers every notion or idea together with its opposite or negation