Monoidal closedness of the category of $\top$-semiuniform convergence spaces

Year 2022, Volume: 51 Issue: 5, 1348 - 1370, 01.10.2022

Lin Zhang Bin Pang

https://doi.org/10.15672/hujms.1065246

Cited By: 7

Abstract

Lattice-valued semiuniform convergence structures are important mathematical structures in the theory of lattice-valued topology. Choosing a complete residuated lattice $L$ as the lattice background, we introduce a new type of lattice-valued filters using the tensor and implication operations on $L$, which is called $\top$-filters. By means of $\top$-filters, we propose the concept of $\top$-semiuniform convergence structures as a new lattice-valued counterpart of semiuniform convergence structures. Different from the usual discussions on lattice-valued semiuniform convergence structures, we show that the category of $\top$-semiuniform convergence spaces is a topological and monoidal closed category when $L$ is a complete residuated lattice without any other requirements.

Keywords

T-semiuniform convergence, T-filter, monoidal closedness, residuated lattice

Supporting Institution

Natural Science Foundation of China

Project Number

12071033，11701122

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