Completeness for Saturated L-Quasi-Uniform Limit Spaces
Subject Areas : Transactions on Fuzzy Sets and Systems
1 - School of Mechanical Engineering, University of Applied Sciences Stralsund, Stralsund, Germany.
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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