---- > [!definition] Definition. ([[universal cover]]) > We say that a [[covering space|covering map]] $p:\widetilde{X} \to X$ is a **universal cover** if $\widetilde{X}$ is [[simply connected]]. > \ > Universal covering is unique up to [[isomorphism of covering spaces|covering space equivalence]], as a corollary of [[The Galois Correspondence for Covering Spaces]]. Thus it makes sense to refer to 'the' [[universal cover]] of a [[topological space|space]]. ^definition ---- #### ---- #### References > [!backlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM [[]] > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ``` > [!frontlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM outgoing([[]]) > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ``` #reformatrevisebatch01