Theorem 1

Let E, B be topological spaces and $p: E\rightarrow B$ a mapping. The following conditions are equivalent:

(i) The space E, endowed with the mapping $p$, is a locally finite covering of B;

(ii) The mapping $p$ is étale, proper and separated;

(iii) The mapping $p$ is continuous, open and separated, its fibres are finite, and the numerical function $b\mapsto$ Card($\overset{-1}{p}(b)$) is upper semicontinuous on B (TG, IV, p. 28).

We shall use the following lemma in the proof: