Configuration space (mathematics)

In mathematics a configuration space (also known as Fadell's configuration space) is any of several constructions closely related to the state space notion in physics. In physics, these are used to describe the state of a whole system as a single point in a high-dimensional space. In mathematics, they are used to describe assignments of a collection of points to positions in a topological space.

For a topological space ${\displaystyle X}$, the n^th (ordered) configuration space of X is the set of n-tuples of pairwise distinct points in ${\displaystyle X}$:

This space is generally endowed with the subspace topology from the inclusion of ${\displaystyle \operatorname {Conf} _{n}(X)}$ into ${\displaystyle X^{n}}$. It is also sometimes denoted ${\displaystyle F(X,n)}$, ${\displaystyle F^{n}(X)}$, or ${\displaystyle {\mathcal {C}}^{n}(X)}$.

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