Completeness of L-quasi-uniform convergence spaces

Document Type : Research Paper


Department of Mathematics, Ocean University of China, Qingdao, 266100, P. R. China


The aim of this paper is to study the completeness of L-quasi-uniform convergence spaces and L-quasi-uniform spaces. Firstly, we describe L-quasi-uniform convergence spaces as enriched categories. Then we give two kinds of completeness of L-quasi-uniform convergence spaces and show that Lawvere completeness implies Cauchy completeness. Finally, we use the Cauchy completeness of L-quasi-uniform convergence spaces to define the Cauchy completeness of L-quasi-uniform spaces, and show that Cauchy completeness is equivalent to Lawvere completeness in L-quasi-uniform spaces.


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