Configuration space of ordered points

Definition
Suppose $$X$$ is a topological space and $$n$$ is a natural number. The configuration space of ordered points $$F_n(X)$$ is defined as follows:


 * As a set, it is the set of ordered $$n$$-tuples of distinct points of $$X$$.
 * The topology is given as follows. First, note that $$F_n(X)$$ is the subset of $$X^n$$ comprising all $$n$$-tuples where no two coordinates are equal, i.e., it is the complement of the fat diagonal. We first give the defining ingredient::product topology on $$X^n$$ and then give $$F_n(X)$$ the defining ingredient::subspace topology arising from that.

Note that the term configuration space is typically used for the configuration space of unordered points $$C_n(X)$$, which is the quotient of this space under the equivalence relation induced by the action of the symmetric group $$S_n$$ by coordinate permutation.