Vol. 61, No. 1, 1975

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Coarse uniform convergence spaces

R. J. Gazik and Darrell Conley Kent

Vol. 61 (1975), No. 1, 143–150

The coarse uniform convergence space is one which is the coarsest member of its convergence class. Each convergence space is compatible with a coarse uniform convergence structure. The regular topological spaces can be characterized as those whose coarse uniform convergence structures are uniformly regular or, equivalently, as those convergence spaces whose coarse uniform convergence structures are very strongly bounded. Every coarse uniform convergence space has a coarse completion. The coarse uniform convergence spaces which have uniformly regular completions are precisely the coarse uniform spaces.

Mathematical Subject Classification 2000
Primary: 54A20
Secondary: 54E15
Received: 30 April 1975
Published: 1 November 1975
R. J. Gazik
Darrell Conley Kent