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⊤-uniform convergence spaces | ||
| Iranian Journal of Fuzzy Systems | ||
| مقاله 11، دوره 19، شماره 2، خرداد و تیر 2022، صفحه 133-149 اصل مقاله (248.8 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2022.6795 | ||
| نویسندگان | ||
| G. J¨ager* 1؛ Y. Yue2 | ||
| 1University of Applied Sciences Stralsund, Stralsund, Germany | ||
| 2School of Mathematical Sciences, Ocean University of China, Qingdao 266100, China | ||
| چکیده | ||
| 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. | ||
| کلیدواژه‌ها | ||
| Topology؛ top-filter؛ uniform convergence space؛ lattice-valued uniform convergence space؛ probabilistic uniform space؛ quantale-valued metric space | ||
| مراجع | ||
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