Geodesic
Zero-dimensionality and Hausdorffness in quantale-valued preordered spaces
Filomat, Tome 36 (2022) no. 7, p. 2311

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DOI

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 T 0 , T 0 , T 1 , pre-T 2 , T 2 and NT 2 quantale-valued preordered spaces. Finally, we examine how these characterization are related to each other and show that the full subcategory T i (pre-T 2 (L-Prord)) (i = 0, 1, 2) of pre-T 2 (L-Prord), and the full subcategory T i (L-Prord) (i = 1, 2) of L-Prord are isomorphic.
DOI : 10.2298/FIL2207311O
Classification : 54A05, 54B30, 54D10, 54A40, 54F45, 18B35
Keywords: Quantale-valued preordered, topological category, zero-dimensionality, pre-Hausdorff, Hausdorff, D-connected 
Samed Özkan; Muhammad Qasim. Zero-dimensionality and Hausdorffness in quantale-valued preordered spaces. Filomat, Tome 36 (2022) no. 7, p. 2311 . doi: 10.2298/FIL2207311O
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     author = {Samed \"Ozkan and Muhammad Qasim},
     title = {Zero-dimensionality and {Hausdorffness} in quantale-valued preordered spaces},
     journal = {Filomat},
     pages = {2311 },
     year = {2022},
     volume = {36},
     number = {7},
     doi = {10.2298/FIL2207311O},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2207311O/}
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