Abstract
The concept of strong soft pre-open set was initiated by Biswas and Parsanann.We utilize this notion to study several characterizations and properties of this set. We investigate the relationships between this set and other types of soft open sets. Moreover, the properties of the strong soft pre-interior and closure are discussed. Furthermore, we define a new concept by using strong soft pre-closed that we denote as locally strong soft pre-closed, in which several results are obtained. We establish a new type of soft pre-open set, namely soft pre-open. Also, we continue to study pre- soft open set and discuss the relationships among all these sets. Some counter examples are given to show some relationships obtained in this work.
Highlights
Moldstov [1] investigated the soft set theory, as a new approach for uncertainties, and the vague set theory
Ogata [5] utilized the idea of operation to introduce new types of open sets, called γ open and pre-γ open sets
We provided several properties and characterizations about pre γ soft open and strong soft γ pre-open sets
Summary
Moldstov [1] investigated the soft set theory, as a new approach for uncertainties, and the vague set theory. A soft set ( ) in soft space ( ) is named pre-soft open if Definition 2.17 [15]. Let γ be soft regular-operation defined over soft topology , the intersection of two soft γ open overis soft γ open set. Proof: Consider ( ) and ( ) are γ soft open sets over space Let 3. Some properties of strong soft γ pre open set Definition 3.1 [6].
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