Timeline for Examples in the vein of smooth manifold + group = Lie group [closed]

Current License: CC BY-SA 3.0

9 events

when toggle format	what		by	license	comment
Apr 25, 2012 at 20:13	vote	accept	Gaussian Eliminator
Apr 25, 2012 at 14:22	comment	added	Gil Kalai		Ordered fields is an example of this nature. To quote wikipedea "In mathematics, an ordered field is a field together with a total ordering of its elements that is compatible with the field operations. Historically, the axiomatization of an ordered field was abstracted gradually from the real numbers, by mathematicians including David Hilbert, Otto Hölder and Hans Hahn. In 1926, this grew eventually into the Artin–Schreier theory of ordered fields and formally real fields." I am not sure there are many definite examples of this kind so this can be a useful question in spite of being vague.
Apr 25, 2012 at 14:13	history	closed	Andy Putman Benoît Kloeckner Marc Palm Igor Rivin Gjergji Zaimi		off topic
Apr 25, 2012 at 14:01	answer	added	Ronnie Brown		timeline score: 4
Apr 24, 2012 at 21:02	comment	added	David Roberts♦		Look up the phrase Lawvere theory. It won't tell you interesting things a bout how the algebraic structure interacts with the ambient structure, but it is a very general version of what you are talking about. That said, I also think this question is too vague.
Apr 24, 2012 at 16:29	comment	added	Marc Palm		Every locally compact group contains an open closed subgroup, which is a projective limit of Lie groups.
Apr 24, 2012 at 16:12	comment	added	Michael Renardy		You could produce a long list of instances where algebraic and topological structure are combined: topological/normed vector spaces, operator semigroups, C*-algebras etc.
Apr 24, 2012 at 16:03	comment	added	Andy Putman		I think this question is too vague, so I voted to close.
Apr 24, 2012 at 15:47	history	asked	Gaussian Eliminator	CC BY-SA 3.0