General topology question

Hello,

I'm reading Hocking & Young's topology again and I've hit upon a kind
of suspect assertion:

"If S is a countably compact T_i space, and f: S->T is continuous and
onto, consider an infinite subset X of T. For each point x in X, select
a point y in S such that f(y) = x. The set of all such points y is an
infinite set Y in S and hence has a limit point p. Continuity then
implies that every open set in T containing f(p) also contains
infinitely many points of X. Thus X has a limit point in T".

I would say the assertion is true only for i>=1. Also, the point of the
theorem is to show that a continuous function maps a countably compact
space onto a countably compact space, and the T_i hypothesis seems
unnecessary. Am I wrong ??

--
Julien Santini

.

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