Affiliations: [a]
Department of Mathematics, Kocaeli University, Kocaeli, Turkey
| [b]
Department of Mathematics, Sana’a University, Sana’a, Yemen
| [c]
Department of Mathematics, College of Sciences and Humanities in Aflaj, Prince Sattam bin Abdulaziz University, Riyadh, Saudi Arabia
| [d]
Department of Algebra and Geometry, Baku State University, Azerbaijan
Correspondence:
[*]
Corresponding author: Abdelwaheb Mhemdi, Department of Mathematics, College of Sciences and Humanities in Aflaj, Prince Sattam bin Abdulaziz University, Riyadh, Saudi Arabia. E-mail: mhemdiabd@gmail.com.
Abstract: A bipolar soft set is given by helping not only a chosen set of “parameters” but also a set of oppositely meaning parameters called “not set of parameters”. It is known that a structure of bipolar soft set is consisted of two mappings such that F : E → P (X) and G :⌉ E → P (X), where F explains positive information and G explains opposite approximation. In this study, we first introduce a new definition of bipolar soft points to overcome the drawbacks of the previous definition of bipolar soft points given in [34]. Then, we explore the structures of bipolar soft locally compact and bipolar soft paracompact spaces. We investigate their main properties and illuminate the relationships between them. Also, we define the concept of a bipolar soft compactification and investigate under what condition a bipolar soft topology forms a bipolar soft compactification for another bipolar soft topology. To elucidate the presented concepts and obtained results, we provide some illustrative examples.
