Geodesic
Epimorphisms From S(X) onto S(Y)
Canadian journal of mathematics, Tome 38 (1986) no. 3, pp. 538-551

Voir la notice de l'article provenant de la source Cambridge University Press

1. Introduction. In this paper, the expression topological space will always mean generated space, that is any T 1 space X for which forms a subbasis for the closed subsets of X. This is not at all a severe restriction since generated spaces include all completely regular Hausdorff spaces which contain an arc as well as all 0-dimensional Hausdorff spaces [3, pp. 198-201], [4].The symbol S(X) denotes the semigroup, under composition, of all continuous selfmaps of the topological space X. This paper really grew out of our efforts to determine all those congruences σ on S(X) such that S(X)/σ is isomorphic to S(Y) for some space Y. 
Jr., K. D. Magill; Misra, P. R.; Tewari, U. B. Epimorphisms From S(X) onto S(Y). Canadian journal of mathematics, Tome 38 (1986) no. 3, pp. 538-551. doi: 10.4153/CJM-1986-026-3
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