Completeness for Saturated L-Quasi-Uniform Limit Spaces

Subject Areas : Transactions on Fuzzy Sets and Systems

Gunther Jager ¹ (School of Mechanical Engineering, University of Applied Sciences Stralsund, Stralsund, Germany.)

Received: 2023-05-14 Accepted : 2023-07-09 Published : 2023-11-07

Keywords: Saturated prefilter, Saturated L-quasi-uniform limit space, Completeness.,

Abstract :

We define and study two completeness notions for saturated 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 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 L-quasi-uniform spaces and that also for saturated L-quasi-uniform limit spaces, both completeness notions are equivalent.

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