---- - Let $X$ and $Y$ be [[topological space]]s. > [!definition] Definition. ([[topological embedding]]) > A **topological embedding** of $X$ in $Y$ is a function $f: X \to Y$ that is a [[homeomorphism]] onto its [[image]]. > \ > Put differently, a [[continuous]] [[injection]] $f:X \to Y$ is bijective when restricted to the function $f':X \to f(X)$. In this case, $f$ is called a **topological embedding** of $X$ in $Y$ provided the inverse $f(X) \to X$ is [[continuous]] also. ---- #### ---- #### 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 > ```