⊤-uniform convergence spaces

Document Type : Research Paper

Authors

1 University of Applied Sciences Stralsund, Stralsund, Germany

2 School of Mathematical Sciences, Ocean University of China, Qingdao 266100, China

Abstract

We show, for a commutative and integral quantale, that the recently introduced  category of $\top$-uniform convergence spaces is a topological category which possesses natural function spaces, making it Cartesian closed. Furthermore, as two important examples for $\top$-uniform convergence spaces, we study probabilistic uniform spaces and quantale-valued metric spaces. The underlying $\top$-convergence spaces are also described and it is shown that in the case of a probabilistic uniform space this $\top$-convergence is the convergence of a fuzzy topology with conical neighbourhood filters. Finally it is shown that the category of $\top$-uniform convergence spaces can be embedded into the category of stratified lattice-valued uniform convergence spaces as a reflective subcategory.

Keywords

References

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Iranian Journal of Fuzzy Systems
Volume 19, Issue 2
March and April 2022
Pages 133-149

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