Fropuff
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The article is indeed a special case for the Euclidean space. But when I wrote the article, there was no "submanifold" article at all - so it's better something than nothing. Also, in physics applications this Euclidean case is often good enough. Your article Submanifold is oriented primarily to the mathematicians - should we put my "Euclidean case" as the example in your article, so the physicists would also be able to find their way through? Thanks, --Sagi Harel 17:25, 12 November 2006 (UTC)
Nice edits on the group action page. Keep up the good work! - grubber 02:52, 5 October 2006 (UTC)
Your question at math help desk
You asked if a top group can be connected but not path connected. I'm a tad impulsive & i just put that stuff w/ a bit more as a question at sci.math.research w/ your handle Fropuff associated. hope u don't mind.Rich 08:21, 17 October 2006 (UTC)
- I don't mind at all. For anyone paying attention, Rich got an answer from Daniel Asimov on sci.math.research who pointed out that the solenoid is a connected topological group (even a compact abelian one) which is not path-connected. I believe the path-component of the identity is dense in this group but I'm not totally sure. -- Fropuff 18:40, 20 October 2006 (UTC)
Coarsest or finest?
I recently edited the disjoint union (topology) page to correct the definition, but that change was reverted so perhaps I should argue the case. The finest topology for which any given map is continuous is the discrete topology so the definition as currently stated is degenerate. We're interested in the smallest (or coarsest) topology for which the canonical injections are continuous. Tim
- No, the finest topology (or final topology) is the correct one. We are concerned with maps where the have a given topology. We are then trying to find a topology on the codomain . If we stick the discrete topology on then these maps may not be continuous. You increase the chances of continuity by coarsening the topology. They will certainly all be continuous when has the trivial topology. So we go for the finest topology for which they are continuous. The coarsest topology (or initial topology) is used when you are trying to putting a topology on the ___domain of a family of functions rather than the codomain. -- Fropuff 16:55, 3 November 2006 (UTC)
