Monoidal closedness of the category of T-semiuniform convergence spaces

Lin Zhang, Bin Pang*

*Corresponding author for this work

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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 T-filters. By means of T-filters, we propose the concept of T-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 T-semiuniform convergence spaces is a topological and monoidal closed category when L is a complete residuated lattice without any other requirements.

Original languageEnglish
Pages (from-to)1348-1370
Number of pages23
JournalHacettepe Journal of Mathematics and Statistics
Volume51
Issue number5
DOIs
Publication statusPublished - Oct 2022

Keywords

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

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Zhang, L., & Pang, B. (2022). Monoidal closedness of the category of T-semiuniform convergence spaces. Hacettepe Journal of Mathematics and Statistics, 51(5), 1348-1370. https://doi.org/10.15672/hujms.1065246