Abstract
It is proved that the quasi-proximity space induced by the bicompletion of a quasi-uniform T 0-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 0 of topological T 0-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 0 is upper K-true if and only if FX is bicomplete whenever X is sober.
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Brümmer, G.C.L., Künzi, HP.A. Bicompletion and Samuel Bicompactification. Applied Categorical Structures 10, 317–330 (2002). https://doi.org/10.1023/A:1015240428548
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DOI: https://doi.org/10.1023/A:1015240428548