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

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,

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Hacettepe Journal of Mathematics and Statistics-Cover

Yayın Aralığı: Yılda 6 Sayı
Başlangıç: 2002
Yayıncı: Hacettepe Üniversitesi Fen Fakultesi

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