A NOTE ON THE RELATIONSHIP BETWEEN HUTTON'S QUASI-UNIFORMITIES AND SHI'S QUASI-UNIFORMITIES

Document Type: Research Paper

Author

Department of Mathematics, Ocean University of China, 238 Songling Road, 266100, Qingdao, P.R.China

Abstract

This note studies the relationship between Hutton's quasi-uniformities and Shi's quasi-uniformities. It is shown that when $L$ satisfies``multiple choice principle" for co-prime elements, the category of Hutton's quasi-uniform spaces is a bireflective full subcategory of the category of Shi's quasi-uniform spaces. Especially, if the remote-neighborhood mapping defined by Shi preserves arbitrary joins, then the two categories are isomorphic to each other.

Keywords


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