Zero-dimensionality and Hausdorffness in quantale-valued preordered spaces-Reference-Cited by-同舟云学术

Zero-dimensionality and Hausdorffness in quantale-valued preordered spaces

Published:2022 Issue:7 Volume:36 Page:2311-2323
ISSN:0354-5180
Container-title:Filomat
language:en
Short-container-title:Filomat

Author:

Özkan Samed¹,Qasim Muhammad²

Affiliation:

1. Department of Mathematics, Nevşehir Hacı Bektas，Veli University, Nevşehir, Turkey

2. Department of Mathematics, School of Natural Sciences, National University of Sciences & Technology, Islamabad, Pakistan

Abstract

In this paper, we study the category of quantale-valued preordered spaces. We show that it is a normalized topological category and give characterization of zero-dimensionality and D-connectedness in the category of quantale-valued preordered spaces. Moreover, we characterize explicitly each of T0, T0, T1, pre-T2, T2 and NT2 quantale-valued preordered spaces. Finally, we examine how these characterization are related to each other and show that the full subcategory Ti(pre-T2(L-Prord)) (i=0,1,2) of pre-T2(L-Prord), and the full subcategory Ti (L-Prord) (i=1,2) of L-Prord are isomorphic.

Publisher

National Library of Serbia

Subject

General Mathematics

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