# Asking hint for a problem

This is my first meta post. I want to ask about one of my deleted post. In that post, I asked for a hint to some problem and gave reasons(brief) why I wasn’t able to solve that problem. To avoid speculation, following is the post:

Let $$Y$$ be compact and $$f: Y\to Y$$ continuous. Prove that there exists a non empty closed set $$A\subseteq Y$$ such that $$A=f(A)$$.

I saw this problem in James Dugundji topology book. Can anyone give some(tiny) hint to solve this problem?

Edit: I don’t know how to solve this “kind” of problem, showing two sets are equal, $$A=f(A)$$. First(& only) thing coming to mind is $$f(Y)$$ is compact, $$A$$ is compact since $$A$$ is closed in $$Y$$, $$f(A)$$ is also compact.

This post got 3 upvote. And answer to that post was also hint(one line). But later that post got deleted by ……… I have some post which are closed, some have net downvote, but those post didn’t get deleted. To be fair, those post have different nature of question than asking hint. So is it appropriate to ask for hint?

• $\exists$ solution to that problem on SE, but I didn’t want to just look up solution without giving my best try. Apr 30 at 8:28
• For the benefit of other people reading this, here is a link to the question mentioned above: Chapter 11, Exercise 10 Section 2 of James Dugundji Topology. (While deleted, it is still visible to the 10k+ users and to the OP.) Apr 30 at 8:30
• @MartinSleziak yeah. Thank you for sharing original post link. Apr 30 at 8:31
• This older discussion is a bit related: Is it okay to ask for a hint to a problem that had already been solved here? (Of course, the site changed a lot since 2015.) I'll also mention that a possible alternative to the main site is asking in one of the chatrooms. Apr 30 at 8:36