[[Group action]]
# Orbit space

Given a group $G$ acting on a space $X$, the **orbit space**[^Bahnenraum] or **quotient** $X / G$ is the set of [[Group action orbit|orbits]] partitioning $X$. #m/def/group
If $X$ is a [[topological space]],
$X / G$ is typically endowed with the [[quotient topology]] induced by the projection $p : x \mapsto Gx$.

[^Bahnenraum]: German _Bahnenraum_.

## Properties

- The [[Orbit space of a properly discontinuous group action]] $X / G$ is a covered by $X$

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#state/tidy | #lang/en | #SemBr