Definition talk:Degenerate Connected Set

Null sets

If we allow topologies over null sets, then if I'm not very much mistaken it holds, without the axiom of choice, that arbitrary products of connected spaces are connected. Otherwise one has to say that if a product of connected spaces is non-empty, then it is connected. --Dfeuer (talk) 03:55, 3 December 2012 (UTC)

Good call. The subject arose when one of the contributor started adding "nonempty" to the invocation of "topological space" in some of the definitions and the proofs. It occurred to me that in most of the standard course texts I'd seen, the subject was not explicitly raised, but the non-empty nature of a space was just taken for granted. I really didn't want to have to go through every page to add "non-empty" to every single page. --prime mover (talk) 06:17, 3 December 2012 (UTC)