@article{article_1065246, title={Monoidal closedness of the category of $\top$-semiuniform convergence spaces}, journal={Hacettepe Journal of Mathematics and Statistics}, volume={51}, pages={1348–1370}, year={2022}, DOI={10.15672/hujms.1065246}, author={Zhang, Lin and Pang, Bin}, keywords={T-semiuniform convergence, T-filter, monoidal closedness, residuated lattice}, 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.}, number={5}, publisher={Hacettepe University}, organization={Natural Science Foundation of China}