# Connected normal space can just be a single point?

Using Urysohn's Lemma, it can be shown that a connected normal space $X$ (with more than one point) is uncountable. But then how can it be that a connected normal space might just be a single point? Is this immediate from Urysohn's Lemma?

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Trivially?${}{}$ –  Asaf Karagila Nov 11 '12 at 22:31
@AsafKaragila: Come again? –  Libertron Nov 11 '12 at 22:32
There is no way of decomposing a singleton into two non-empty disjoint sets... everything much hold vacuously. –  Asaf Karagila Nov 11 '12 at 22:33
Urysohn makes no (nonvacuous) statement about one-point spaces. But the very definition of normal is trivially verified for one-point space. –  Hagen von Eitzen Nov 11 '12 at 22:33