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

Qiu Jin,Lingqiang Li,Guangming Lang

doi:10.3390/math7040370

Qiu Jin, Lingqiang Li + Show 1 more

Open Access

https://doi.org/10.3390/math7040370

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Abstract

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.

Highlights

Convergence spaces [1] are generalizations of topological spaces
Regularity in >-convergence spaces by different diagonal conditions of >-filters were researched by Fang [31] and Li [42], respectively
Let {( Xi, qi, pi )}i∈ I be pairs of >-convergence spaces such that each qi is pi -regular

Summary

Introduction

Convergence spaces [1] are generalizations of topological spaces. Regularity is an important property in convergence spaces. Wilde-Kent [6] further presented a theory of lower and upper p-regular modifications in convergence spaces. L-convergence spaces) was studied by Jäger [37] (resp., Boustique-Richardson [38,39]), p-regularity and p-regular modifications in stratified L-generalized convergence spaces and that in stratified. Regularity in >-convergence spaces by different diagonal conditions of >-filters were researched by Fang [31] and Li [42], respectively. >-convergence spaces by closure condition of >-filters were studied by Reid and Richardson [36]. The lower and upper p-regular modifications in >-convergence spaces are investigated and researched. It is shown that lower (resp., upper) p-regular modification and final (resp., initial) structures have good compatibility

Preliminaries

Lower p-Regular Modification

Upper p-Regular Modification

Conclusions