Are there any countable Hausdorff connected spaces?

Question

Do countable Hausdorff connected topological spaces exist?

Answer 1

Yes, see here (MathOverflow) for references to some non-trivial examples.

Answer 2

Trivially yes, a singleton for example ;). Non-trivial examples abound, for example ''A countable connected Hausdorff space'' by Brown, in Bull. Amer. Math. Soc., 59 (1953) p. 367.