Completions of ⊤-quasi-Cauchy spaces

Document Type : Original Manuscript


University of Applied Sciences Stralsund, Stralsund, Germany


In the category of ⊤-quasi-Cauchy spaces, completeness and completion can be studied in a non-symmetric framework encompassing ⊤-quasi-uniform (limit) spaces. Based on constructions by E.E. Reed in the category of Cauchy spaces and, recently, by L. Reid and G. Richardson in the category of ⊤-Cauchy spaces, we give a family of completions for a non-complete ⊤-quasi Cauchy space. As particular instances we study pretopological and topological completions of ⊤-quasi-Cauchy spaces.


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