Geodesic
Monomorphisms of Semigroups of Local Dendrites
Canadian journal of mathematics, Tome 38 (1986) no. 4, pp. 769-780

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

When we speak of the semigroup of a topological space X, we mean S(X) the semigroup of all continuous self maps of X. Let h be a homeomorphism from a topological space X onto a topological space Y. It is immediate that the mapping which sends f ∊ S(X) into h o f o h −1 is an isomorphism from the semigroup of X onto the semigroup of Y. More generally, let h be a continuous function from X into Y and k a continuous function from Y into X such that k o h is the identity map on X. One easily verifies that the mapping which sends f into h o f o k is a monomorphism from S(X) into S(Y). Now for “most” spaces X and Y, every isomorphism from S(X) onto S(Y) is induced by a homeomorphism from X onto Y. Indeed, a number of the early papers dealing with S(X) were devoted to establishing this fact. 
JR., K. D. Magill. Monomorphisms of Semigroups of Local Dendrites. Canadian journal of mathematics, Tome 38 (1986) no. 4, pp. 769-780. doi: 10.4153/CJM-1986-040-2
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