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Results tagged with infinite-dimensional-manifolds
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user 61536
19
votes
Accepted
Does $\mathbb C\mathbb P^\infty$ have a group structure?
I noticed that this question still has no accepted answer and all existing answers are rather long. It seems that the answer can be easily obtained using some results of infinite-dimensional topology, …
- 41.8k
8
votes
Accepted
Sequences with 0's in $\mathbb R ^\omega$
For every $n\in\mathbb N$ consider the space
$$X_n=\{x\in\mathbb R^\omega:\lvert x^{-1}(0)\rvert\ge n\}.$$
Theorem. For any positive integer numbers $n<m$, the spaces $X_n$ and $X_m$ are not homeomorp …
- 41.8k
6
votes
Accepted
Are infinite simplicial complexes all manifolds?
This question concerns manifolds modeled on the direct limit $\mathbb R^\infty$ of Euclidean spaces. The theory of such manifolds is well-developed. The most important results of this theory were obta …
- 41.8k