Compactness Theorem (Propositional Logic) and Compactness (Metric spaces).
19209
Why is compactness in logic called compactness?
107772
Separability of functions with compact support
65358
Prove $X$ is compact iff for each family $\{ F_\alpha\}_{\alpha\in I}$ of closed subsets of $X$ with the FIP, we have $\cap F_\alpha\neq\varnothing$.
3708
How can I prove that compact subset iff sequentially compact in second countable topological spaces?
147331
Compactness and Hausdorffness
39076
Contraction of compact sets
121135
Why don't we use closed covers to define compactness of metric space?
126944
Metric spaces problem
22131
Prove if nonempty $K \subset\mathbb{R}$ is compact, then both sup $K$ and inf $K$ exist and are elements of $K$.
67050
Every separable metric space has a countable base
66550
Cardinality of separable metric spaces
126759
Unbounded continuous function on non-compact metric space
146967
Understanding equivalent metric spaces
83159
Defining a metric space
138607
Proof that a limit point compact metric space is compact.
151832
uniformly convergence on compact metric space
6210
Countable compact spaces as ordinals