International Journal of Mathematics and Mathematical Sciences
Volume 7 (1984), Issue 4, Pages 663-666

The largest proper congruence on S(X)

K. D. Magill Jr.

Department of Mathematics, State University of New York at Buffalo, 106 Diefendorf Hall, Buffalo 14214-3093, New York, USA

Received 3 March 1984

Copyright © 1984 K. D. Magill. 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.


S(X) denotes the semigroup of all continuous selfmaps of the topological space X. In this paper, we find, for many spaces X, necessary and sufficient conditions for a certain type of congruence to be the largest proper congruence on S(X).