\begin{definition}[Definition:Partition of Unity (Topology)/Subordinate]
Let $X$ be a topological space.
Let $\AA = \set {\phi_\alpha : \alpha \in A}$ be a partition of unity.
Let $\BB = \set {U_\beta: \beta \in B}$ be an open cover of $X$.
Let the set $\set {\map \supp {\phi_\alpha}^\circ: \alpha \in A}$ of interiors of supports be a refinement of $\BB$.
Then $\AA$ is said to be '''subordinate''' to the cover $\BB$.
Category:Definitions/Topology
\end{definition}