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I learned a lie group is a group which satisfied all the conditions of a diferentiable manifold. that is the real rigour definition or just a simplified one?
thanks
thanks
Uh, that is not necessarily true. But it is true that things are well-behaved only on topological manifolds. A differentiable structure can be put on very general spaces however. https://arxiv.org/abs/0807.1704It is possible to have a DS only on a topological space that is a topological manifold
Mathematicians have a strange kind of humor: "Convenient Category". Considering axiom 3 of Chen-spaces and the following examples I'm curious to see what will be left under so much generalization.Uh, that is not necessarily true. But it is true that things are well-behaved only on topological manifolds. A differentiable structure can be put on very general spaces however. https://arxiv.org/abs/0807.1704
Surprisingly much actually...Mathematicians have a strange kind of humor: "Convenient Category". Considering axiom 3 of Chen-spaces and the following examples I'm curious to see what will be left under so much generalization.