Prove that an infinite chain of proper containments of compact sets is non empty
103383
Let $\{K_i\}_{i=1}^{\infty}$ a decreasing sequence of compact and non-empty sets on $\mathbb{R}^n.$ Then $\cap_{i = 1}^{\infty} K_i \neq \emptyset.$
107641
Show that an infinite set of families are linearly independent
44974
Infinite set and countable subsets
66398
Union of a finite set and a countably infinite set is countably infinite
125411
Infinite set always has a countably infinite subset
8015
Compact set plus a closed set is a closed set
102113
Proof that the number of proofs is countably infinite
97761
Show that a proper continuous map from $X$ to locally compact $Y$ is closed
88099
Not $\sigma$-compact set without axiom of choice
97064
Dense set in an infinite cofinite space
58285
Is it true that if $X$ is connected, then for every nonempty proper subset $A$ of $X$, we have $\mathbf{Bd} \ne \emptyset$
9268
Proving that the Union of Two Compact Sets is Compact
128437
How to prove that a finite set is countable
153573
Counter Example for the union of any number of compact sets is compact in T2-spaces
91237
Every infinite set contains a countable subset
119624
A Dedekind infinite set has a countably infinite proper subset
45792
Rigorous proof that surjectivity implies injectivity for finite sets