# Category:Compactness theorems

Computing portal |

Here is a list of articles in the Compactness theorems category of the Computing portal that unifies foundations of mathematics and computations using computers. In mathematics, specifically in topology and functional analysis, compactness theorems provide necessary or sufficient conditions for the compactness of a set.

## Pages in category "Compactness theorems"

The following 18 pages are in this category, out of 18 total.

### A

- Arzelà–Ascoli theorem
*(computing)*

### B

- Banach–Alaoglu theorem
*(computing)* - Blaschke selection theorem
*(computing)* - Bolzano–Weierstrass theorem
*(computing)*

### C

- Cantor's intersection theorem
*(computing)*

### E

- Eberlein–Šmulian theorem
*(computing)*

### F

- Fraňková–Helly selection theorem
*(computing)* - Fréchet–Kolmogorov theorem
*(computing)*

### G

- Gromov's compactness theorem (topology)
*(computing)*

### H

- Heine–Borel theorem
*(computing)* - Helly's selection theorem
*(computing)*

### M

- Mahler's compactness theorem
*(computing)* - Mazur's lemma
*(computing)* - Michael selection theorem
*(computing)* - Montel's theorem
*(computing)* - Mumford's compactness theorem
*(computing)*

### P

- Prokhorov's theorem
*(computing)*

### S

- Sobolev inequality
*(computing)*