AbstractsBiology & Animal Science

Completeness and related topics in a quasi-uniform space

by John Warnock Carlson

Institution: Missouri University of Science and Technology
Year: 1970
Record ID: 1509711
Full text PDF: http://hdl.handle.net/10355/36797


"Completions and a strong completion of a quasi-uniform space are constructed and examined. It is shown that the trivial completion of a T₀ space is T₀ . Examples are given to show that a T₁ space need not have a T₁ strong completion and a T₂ space need not have a T₂ completion. The nontrivial completion constructed is shown to be T₁ if the space is T₁ and the quasi-uniform structure is the Pervin structure. It is shown that a space can be uniformizable and admit a strongly complete quasi-uniform structure and not admit a complete uniform structure. Several counter-examples are provided concerning properties which hold in a uniform space but do not hold in a quasi-uniform space. It is shown that if each member of a quasi-uniform structure is a neighborhood of the diagonal then the topology is uniformizable" – Abstract, page ii.