Geodesic
Homomorphisms from S(X) into S(Y)
Canadian journal of mathematics, Tome 29 (1977) no. 3, pp. 615-625

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

S(X) is the semigroup under composition of all continuous selfmaps of the topological space X. For certain spaces X and Y we classify completely the homomorphisms from S(X) into S(Y). An application of the main result to S(I) the semigroup of all continuous selfmaps of the closed unit interval I results in the solution of a problem which was suggested in the closing paragraph of [6]. 
Magill, Kenneth D. Homomorphisms from S(X) into S(Y). Canadian journal of mathematics, Tome 29 (1977) no. 3, pp. 615-625. doi: 10.4153/CJM-1977-062-0
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