Definition

Covering Space

Lie Groups and Lie Algebras · lie-groups.tex

A continuous map $p : \widetilde{X} \to X$ (Definition~Continuous Map and Homeomorphism) between topological spaces (Definition~Topological Space) is a covering map if every point $x \in X$ has an open neighbourhood $U$ such that $p^{-1}(U)$ is a disjoint union of open sets each mapped homeomorphically to $U$ by $p$. The universal cover $\widetilde{X}$ is the unique (up to isomorphism) simply connected (Definition~Simply Connected) covering space of $X$.

Depends on

Used in

Universal Cover of a Lie Group

Dependency Graph

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