On Fri, 30 Apr 2004 20:55:45 -0700, firstname.lastname@example.org wrote:
>On Fri, 30 Apr 2004 18:51:26 -0700, email@example.com wrote: > >[snip] > >>>"Homomorphism theorem"? Is this what's called "Dimension Theorem" now? >> >>No, it's something in group theory. Not entirely unrelated, though. > >I have this uneasy feeling about what I said here -- not that I struck >out, but rather, that I fouled off a fat pitch that I shoulda hit out >of the park. IOW, the feeling that "not entirely unrelated" is an >understatement, and that the connections are in fact deep. I better >go off to plough thru my Herstein and see to what degree this is >really so. > >Of course, dimension is strictly a vector-space thingy and so maybe
To quiet some potential boos, I should clarify -- here I meant only that a vector space's dimension is not one of that space's *group* properties.
>that's why I'm not getting booed out of the park quite yet. I hope. >Um, comments?
Never mind the comments, I see that I was right. (Both times. :-) My own comments about quotient spaces, in a separate branch of this thread, are sufficient commentary for my needs, I think.
Then again, if somebody still has something pithy to add from category theory or whatever, I won't mind that at all. I am still learning this stuff.