Completion in a common supercategory of Met, UAP, wsAP and Near

Demonstratio mathematica

article

Mona Khare¹  Surabhi Tiwari¹ 

[1] Department of Mathematics, University of Allahabad

关键词: grill;    approach space;    approach nearness;    lattice structure;    completion;   

DOI  :  10.1515/dema-2013-0435

学科分类：外科医学

来源: De Gruyter

【 摘 要 】

This paper investigates the notion of approach nearness spaces. Using clusters, completion of an approach nearness space is constructed, which is a unified study of completion in the context of metric spaces, uniform approach spaces, weakly symmetric approach spaces and nearness spaces. Another generalization of completeness, called ultrafilter completeness is introduced to prove the Niemytzki–Tychonoff theorem for approach nearness spaces. Both definitions of completions are shown to be equivalent in a limit-regular approach space. Various examples are given to support the present study.

【 授权许可】

CC BY