Definition

Compactness

Lie Groups and Lie Algebras · lie-groups.tex

A topological space $X$ (Definition~Topological Space) is compact if every open cover of $X$ has a finite subcover. A subset $A \subseteq \mathbb{R}^n$ is compact if and only if it is closed and bounded (Heine--Borel).

Depends on

Topological Space

Used in

Maschke's Theorem for Compact Groups
Proposition

Dependency Graph

flowchart LR classDef current fill:#6366f1,color:#fff,stroke:#4f46e5 nc9093e38["Topological Space"] n5d29db29["Compactness"]:::current n692f1650["Maschke's Theorem for Compact Groups"] n8aabc776["Proposition"] nc9093e38 --> n5d29db29 n5d29db29 --> n692f1650 n5d29db29 --> n8aabc776 click nc9093e38 "../objects/c9093e38.html" "_self" click n692f1650 "../objects/692f1650.html" "_self" click n8aabc776 "../objects/8aabc776.html" "_self"