12:15 PM
A new tag was created by Lao-tzu.
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I want to know if profinite sets have the following properties: any surjective family of continuous maps $V_i\to U$ of profinite sets has a subfamily which is already a surjective family? This is to be compared with this result. a continuous map between profinite sets is an open map? any open s...

I do not know anything about profinite sets. (In fact, I haven't heard much about profinite groups either - but I know that name and I know that there is such tag both here and on MO.)

8 hours later…
8:02 PM
A new tag was created by Shootforthemoon.
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If a function is the composition of two continuous functions, it is also continuous on its domain. Is the reverse true? I mean if a function can be rewritten as the composition of any two other functions and is continuous, then are the other two also continuous? In other words, is the comp...

I am not really sure whether such tag might be useful. But even if it would be useful on some questions, I don't see why exactly it would fit here.

@MartinSleziak The post has been deleted by the author, so presumably the tag will die eventually.