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Results tagged with topological-groups
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user 23571
A topological group is a group $G$ together with a topology on the elements of $G$ such that the group operation and group inverse function are both continuous (with respect to the topology).
18
votes
Topological structure of SO(n) as a product
Another line of reasoning: If $SO(n)$ were homeomorphic to the product $S^{n-1}\times SO(n-1)$ then $S^{n-1}$ would be a retract (not deformation retract!) of $SO(n)$, hence $S^{n-1}$ would be an H-sp …
- 20k
7
votes
When are the homology and cohomology Hopf algebras of topological groups equal?
The example of $\mathrm{SO}_n$ that Torsten Ekedahl gives is quite instructive. Taking the union over all $n$, the infinite-dimensional group $\mathrm{SO}$ has mod $2$ cohomology a polynomial ring wit …
- 20k