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Pre-Hausdorffness and Hausdorffness in Quantale-Valued Gauge Spaces

Author

Listed:
  • 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)

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.

Suggested Citation

  • Samed Özkan & Samirah Alsulami & Tesnim Meryem Baran & Muhammad Qasim, 2022. "Pre-Hausdorffness and Hausdorffness in Quantale-Valued Gauge Spaces," Mathematics, MDPI, vol. 10(24), pages 1-14, December.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:24:p:4819-:d:1007557
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