Talk:Sierpiński space

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[edit] Weak topology

The current version of the article states that:

• If X is a topological space with topology T, then the weak topology on X generated by C(X,S) coincides with T.

Is this true? I would say it holds only for T₀-spaces. The 2-point indiscrete space could be a counterexample. --Kompik 18:56, 23 February 2006 (UTC)

Surely for an indiscrete space (X,T), the weak topology on X generated by any set of continuous functions on X is still T, since the indiscrete topology is the weakest possible tolopogy on X. Martin Orr 21:43, 24 May 2006 (UTC)