---- > [!definition] Definition. ([[local homeomorphism]]) > A function $f:X \to Y$ between [[topological space|topological spaces]] $X$ and $Y$ is called a **local homeomorphism** if every point of $X$ has a [[neighborhood]] $U$ whose image $f(U)$ is open in $Y$ and the restriction $f |_{U}:U \to f(U)$ is a [[homeomorphism]] (where the respective [[subspace topology|subspace topologies]] are used on $U$ and on $f(U)$). ---- #### ---- #### 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 > ```