The abstract of the talk (see below) may be downloaded in one of the following formats:

Every continuous map $X\to Y$ defines, by composition, a homomorphism
between the corresponding algebras of real-valued continuous functions
$C(Y)\to C(X)$. By means of this homomorphism, $C(X)$ is a $C(Y)$-algebra.

In this work, we study when is $C(X)$  single generated as $C(Y)$-algebra,
that is, when does exist a function $f\in C(X)$ such that $C(X)=C(Y)[f]$.

We shall prove, for compact spaces $X$ and $Y$, that if $C(X)=C(Y)[f]$, then
the map $X\to Y$ is locally injective.

We shall give examples of locally injective continuous maps, between compact
spaces $X\to Y$ such that $C(X)$, with the structure of $C(Y)$-algebra
induced by the composition morphism $C(Y)\to C(X)$, is not single generated.

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