Is it permissible to repost a problem that hasn't been solved in the desired way?

I'm thinking of a particular example to show that

there isn't a sequence of continuous function on $[0,1]$ that converges pointwise to the function $f$ on $[0,1]$ defined by $f(x)=0$ if $x$ is rational and $f(x)=1$ if $x$ is irrational.

However, the only answer provided invoked Baire's theorem, which seems like unnecessary machinery. I'm wondering about a solution that only uses the definition of continuity and point-wise convergence.

This is a slightly different question. Is there any consensus on how I should propose further inquiry into the question?

• Definitely provide a link from your second question to your first one in the question body; it would help answerers to see that suggesting "But, Baire's theorem really is the way to do that" isn't helpful as well as avoid duplicated effort. (It's probably worth it to put links both ways, really) – Milo Brandt Dec 30 '15 at 6:44
• @MiloBrandt I have added the link to the question, as you recommended. – Martin Sleziak Dec 30 '15 at 10:19

• It's not that much of an abstraction to say that $[0,1]$ cannot be written as a countable union of closed sets with empty interior. – user147263 Dec 30 '15 at 5:21