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Results tagged with compactifications
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user 14094
7
votes
Accepted
Are countable FC-groups maximally almost periodic?
Here's a counterexample. Consider a non-abelian finite, 2-step nilpotent group $F$. Let $Z$ be its derived subgroup. Define $G$ as the quotient of the direct sum $F^{(\mathbf{N})}=\bigoplus F_n$ of co …
- 63.9k
14
votes
Accepted
Do all homogeneous spaces have homogeneous compactifications?
Since you want a connected example:
A surface of infinite genus has no homogeneous compactification.
Indeed first observe a dense locally compact subset has to be open.
So the surface has to be open, …
- 63.9k