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Results tagged with compactifications
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user 4832
12
votes
Do all homogeneous spaces have homogeneous compactifications?
The countable discrete space $\omega$ is a counterexample.
Suppose $Y$ is a homogeneous compactification of $\omega$, with $X \subset Y$ being homeomorphic to $\omega$. As $Y$ is infinite, it necessa …
- 29.7k
2
votes
Accepted
Two questions related to Dirichlet spaces and Sobolev spaces
For question 2, if you had $\Omega$ in place of $\bar{\Omega}$, the conditions you state would still be satisfied, but there are other interesting conditions that would not be. It would fail to be a …
- 29.7k