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⊤-uniform convergence spaces

Year: 1401
COI: JR_IJFS-19-2_011
Language: EnglishView: 64
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G. J¨ager - University of Applied Sciences Stralsund, Stralsund, Germany
Y. Yue - School of Mathematical Sciences, Ocean University of China, Qingdao ۲۶۶۱۰۰, China


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.


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J¨ager, G. and Yue, Y.,1401,⊤-uniform convergence spaces,

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