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Mathematics 2019, 7(3), 228; https://doi.org/10.3390/math7030228

p-Topologicalness—A Relative Topologicalness in ⊤-Convergence Spaces

Department of Mathematics, Liaocheng University, Liaocheng 252059, China
Received: 24 January 2019 / Revised: 16 February 2019 / Accepted: 25 February 2019 / Published: 1 March 2019
(This article belongs to the Special Issue Fuzzy Sets, Fuzzy Logic and Their Applications)
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Abstract

In this paper, p-topologicalness (a relative topologicalness) in ⊤-convergence spaces are studied through two equivalent approaches. One approach generalizes the Fischer’s diagonal condition, the other approach extends the Gähler’s neighborhood condition. Then the relationships between p-topologicalness in ⊤-convergence spaces and p-topologicalness in stratified L-generalized convergence spaces are established. Furthermore, the lower and upper p-topological modifications in ⊤-convergence spaces are also defined and discussed. In particular, it is proved that the lower (resp., upper) p-topological modification behaves reasonably well relative to final (resp., initial) structures. View Full-Text
Keywords: fuzzy topology; fuzzy convergence; lattice-valued convergence; ⊤-convergence space; relative topologicalness; p-topologcalness; diagonal condition; neighborhood condition fuzzy topology; fuzzy convergence; lattice-valued convergence; ⊤-convergence space; relative topologicalness; p-topologcalness; diagonal condition; neighborhood condition
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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Li, L. p-Topologicalness—A Relative Topologicalness in ⊤-Convergence Spaces. Mathematics 2019, 7, 228.

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