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Bicompletion and Samuel Bicompactification.

Authors :
Brümmer, G.
Künzi, H.-P.
Source :
Applied Categorical Structures; Jun2002, Vol. 10 Issue 3, p317-330, 14p
Publication Year :
2002

Abstract

It is proved that the quasi-proximity space induced by the bicompletion of a quasi-uniform T<subscript>0</subscript>-space X is a subspace of the quasi-proximity space induced by the Samuel bicompactification of X. The result is then used to establish that the locally finite covering quasi-uniformity defined on the category Top<subscript>0</subscript> of topological T<subscript>0</subscript>-spaces and continuous maps is not lower K-true (in the sense of Brümmer). It is also shown that a functorial quasi-uniformity F on Top<subscript>0</subscript> is upper K-true if and only if FX is bicomplete whenever X is sober. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
09272852
Volume :
10
Issue :
3
Database :
Complementary Index
Journal :
Applied Categorical Structures
Publication Type :
Academic Journal
Accession number :
51582957
Full Text :
https://doi.org/10.1023/A:1015240428548