I believe regular epimorphisms in the category of topological groups are precisely the surjective open maps. Is this also true for the category of topological rings? If not, is there some other characterization of the regular epimorphisms in TopRing? A reference would be very much appreciated.
This question is now cross-posted at MathOverflow:
https://mathoverflow.net/questions/416708/regular-epimorphisms-in-the-category-of-topological-rings