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Unit Partition in Mathematics 📂Set Theory

Unit Partition in Mathematics

Definition

A set $\left\{ u_{\alpha} \right\}_{\alpha \in \Lambda}$ of continuous functions $u_{\alpha} : X \to [0,1], \alpha \in \Lambda$ that satisfies the conditions below is called a Partition of Unity.
$$ \sum _{\alpha \in \Lambda}u_{\alpha}(x)=1 $$