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

Authors : Lin ZHANG, Bin PANG

Pages : 1348-1370

Doi:10.15672/hujms.1065246

View : 26 | Download : 10

Publication Date : 2022-10-01

Article Type : Research Paper

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