‎Completeness for Saturated $\mathsf{L}$-Quasi-Uniform Limit Spaces

Transactions on Fuzzy Sets and Systems

مقاله 8، دوره 2، شماره 2، بهمن 2023، صفحه 127-136   

نوع مقاله: Original Article

شناسه دیجیتال (DOI): 10.30495/tfss.2023.1986166.1070

نویسنده

Gunther Jäger^*

School of Mechanical Engineering, University of Applied Sciences, Stralsund Stralsund, Germany.

چکیده

‎We define and study two completeness notions for saturated $\mathsf{L}$-quasi-uniform limit spaces‎. ‎The one‎, ‎that we term Lawvere completeness‎, ‎is defined using the concept of promodule and lends a lax algebraic interpretation of completeness also for saturated $\mathsf{L}$-quasi-uniform limit spaces‎. ‎The other‎, ‎termed Cauchy completeness‎, ‎is defined using saturated Cauchy pair prefilters‎. ‎We show that both concepts coincide with related notions in the case of saturated $\mathsf{L}$-quasi-uniform spaces and that also for saturated $\mathsf{L}$-quasi-uniform limit spaces‎, ‎both completeness notions are equivalent‎.

کلیدواژه‌ها

Saturated prefilter‎؛ ‎Saturated L-quasi-uniform limit space‎؛ ‎Completeness‎

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