Here's a theorem in the course notes of a course on Polish groups: Let $X$ and $Y$ be Polish spaces and $f:X\to Y$ continuous. $f(X)$ has the Baire property. In the course note, it's written that this follows from the existence of $U(A)$ (which I define bellow). The proof should be eas...

I noticed that a new tag has been created this year, apparently in February. I first noticed it today, while reviewing a suggested tag-wiki for the tag. I do not think the coincidences tag is necessary, nor helpful. If users could add up to ten tags on any question, then perhaps it doesn't h...