Subcategories of the category of $\top$-convergence spaces

Year 2024, Volume: 53 Issue: 1, 88 - 106, 29.02.2024

Yuan Gao Bin Pang

https://doi.org/10.15672/hujms.1205089

Abstract

$\top$-convergence structures serve as an important tool to describe fuzzy topology. This paper aims to give further investigations on $\top$-convergence structures. Firstly, several types of $\top$-convergence structures are introduced, including Kent $\top$-convergence structures, $\top$-limit structures and principal $\top$-convergence structures, and their mutual categorical relationships as well as their own categorical properties are studied. Secondly, by changing of the underlying lattice, the ``change of base" approach is applied to $\top$-convergence structures and the relationships between $\top$-convergence structures with respect to different underlying lattices are demonstrated.

Keywords

T-convergence structure, T-filter, Kent convergence, limit structure, change of base

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