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p-Regularity and p-Regular Modification in ⊤-Convergence Spaces

1,*, 1,2,3,* and 2,3
Department of Mathematics, Liaocheng University, Liaocheng 252059, China
School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha 410114, China
Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science and Technology, Changsha 410114, China
Authors to whom correspondence should be addressed.
Mathematics 2019, 7(4), 370;
Received: 9 March 2019 / Revised: 19 April 2019 / Accepted: 22 April 2019 / Published: 24 April 2019
(This article belongs to the Special Issue Fuzzy Sets, Fuzzy Logic and Their Applications)
PDF [280 KB, uploaded 24 April 2019]


Fuzzy convergence spaces are extensions of convergence spaces. ⊤-convergence spaces are important fuzzy convergence spaces. In this paper, p-regularity (a relative regularity) in ⊤-convergence spaces is discussed by two equivalent approaches. In addition, lower and upper p-regular modifications in ⊤-convergence spaces are further investigated and studied. Particularly, it is shown that lower (resp., upper) p-regular modification and final (resp., initial) structures have good compatibility. View Full-Text
Keywords: fuzzy topology; fuzzy convergence; ⊤-convergence space; regularity fuzzy topology; fuzzy convergence; ⊤-convergence space; regularity
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

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Jin, Q.; Li, L.; Lang, G. p-Regularity and p-Regular Modification in ⊤-Convergence Spaces. Mathematics 2019, 7, 370.

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