Definition: In mathematics, a nonlocally defined space (also known as an uncountable locally countably infinite space) is a topological space that has no finite subspaces. That means it can be represented by a union of countably many open sets without any choice. For example: 1. The real line $\mathbb{R}$ is nonlocally defined because there are infinitely many open intervals in the plane $(0, 1)$. 2. The complex numbers $\mathbb{
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