模糊拟一致收敛空间的完备性

Completeness of Fuzzy Quasi-uniform Convergence Spaces

本文借助饱和预滤将模糊拟一致收敛空间视为强化范畴,讨论了模糊拟一致收敛空间的完备性,证明了模糊拟一致空间是Cauchy完备的当且仅当其生成的模糊拟一致收敛空间是Cauchy完备的,还证明了模糊拟一致收敛空间Lawvere完备性与Cauchy完备性之间的等价性。

In this paper,fuzzy quasi-uniform convergence spaces are regarded as enriched category by using the saturated prefilter.Then the completeness of fuzzy quasi-uniform convergence spaces is discussed.Furthermore,we prove that the fuzzy quasi-uniform spaces are Cauchy completeness if and only if the fuzzy quasi-uniform convergence spaces it generates are Cauchy completeness,and we also prove that the Lawvere completeness and Cauchy completeness of fuzzy quasi-uniform convergence spaces is equivalent.