Mathematics (Dec 2022)

Pre-Hausdorffness and Hausdorffness in Quantale-Valued Gauge Spaces

  • Samed Özkan,
  • Samirah Alsulami,
  • Tesnim Meryem Baran,
  • Muhammad Qasim

DOI
https://doi.org/10.3390/math10244819
Journal volume & issue
Vol. 10, no. 24
p. 4819

Abstract

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In this paper, we characterize each of T0, T1, 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 T0, T1 and T2 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