---- > [!definition] Definition. ([[singular simplex]]) > A **singular $n$-simplex** in a [[topological space]] $X$ is a [[continuous]] map $\sigma$ from the [[simplex|standard simplex]] $\Delta^{n}$ into $X$. ^definition > [!intuition] > The word 'singular' is used because $\sigma$ need not be [[injection|injective]] (and can therefore have 'singular points' of intersection). ^intuition ---- #### ---- #### 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 > ```