Let $p:X \rightarrow Y$ be a perfect map. Show that if $X$ is locally compact then so is $Y$.
103451
Show that $Y$ is locally compact.
121957
Is $p\mapsto \|f\|_p$ continuous?
146146
Proof that a closed subset of a compact space is a compact space
143043
When is a local homeomorphism a covering map?
47251
Non-compactness of $\mathbb{R}$ with the cocountable topology
28637
Proving continuous image of compact sets are compact
47
Let $f$ be a continuous and open map from $\mathbb R $ to $\mathbb R$.Prove that $f$ is monotonic.
39843
Let $P$ be a prime. Show that $\exists$ $x \in \mathbb{N}$ such that $f(x) = p$ then $\exists$ $y \in \mathbb{N}$ such that $g(y) = p$
94485
Limit point compactness implies compactness.
128730
Open subspaces of locally compact Hausdorff spaces are locally compact
50611
Question about Stone-Čech compactification
63529
How to show that this set is compact in $\ell^2$
131637
Real projective space is Hausdorff: is this proof correct?
98609
Does pointwise equicontinuous and uniformly equicontinuous implies compactness?
69650
In $\mathbb{R}^n$, locally lipschitz on compact set implies lipschitz
121395
Let $X$ and $Y$ be non-empty sets and let $f:X \rightarrow Y$. Prove that $ f^{ −1} :P(Y ) → P(X) $ is injective if, and only if, $f$ is surjective.
3708
How can I prove that compact subset iff sequentially compact in second countable topological spaces?