Pre-Hausdorffness and Hausdorffness in Quantale-Valued Gauge Spaces

Samed Özkan, Samirah Alsulami, Tesnim Meryem Baran and Muhammad Qasim ()
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Samed Özkan: Department of Mathematics, Nevşehir Hacı Bektaş Veli University, Nevşehir 50300, Turkey
Samirah Alsulami: Department of Mathematics, Collage of Science, University of Jeddah, Jeddah 21577, Saudi Arabia
Tesnim Meryem Baran: MEB, Kayseri 38170, Turkey
Muhammad Qasim: Department of Mathematics, National University of Sciences & Technology (NUST), H-12 Islamabad 44000, Pakistan

Mathematics, 2022, vol. 10, issue 24, 1-14

Abstract: In this paper, we characterize each of T 0 , T 1 , Pre-Hausdorff and Hausdorff separation properties for the category L - GS of quantale-valued gauge spaces and L -gauge morphisms. Moreover, we investigate how these concepts are related to each other in this category. We show that T 0 , T 1 and T 2 are equivalent in the realm of Pre-Hausdorff quantale-valued gauge spaces. Finally, we compare our results with the ones in some other categories.

Keywords: ?-gauge space; topological category; separation; Hausdorffness (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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