International Journal of Mathematics and Mathematical Sciences
Volume 11 (1988), Issue 3, Pages 503-506

The Smirnov compactification as a quotient space of the Stone-Čech compactification

T. B. M. McMaster

Pure Mathematics Department, Queen' s University, Belfast BT7 1NN, Ireland

Received 18 March 1987; Revised 1 June 1987

Copyright © 1988 T. B. M. McMaster. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


For a separated proximity space, a decomposition of the Stone-Čech compactification is presented which produces the Smirnov compactification and its basic properties by elementary arguments without recourse to clusters or totally bounded uniformities.