# Definition:Region/Plane

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## Definition

A point set $R$ in the plane is a **region** if and only if:

- $(1): \quad$ Each point of $R$ is the center of a circle all of whose elements consist of points of $R$
- $(2): \quad$ Each point of $R$ can be joined by a curve consisting entirely of points of $R$.

## Sources

- 1963: Morris Tenenbaum and Harry Pollard:
*Ordinary Differential Equations*... (previous) ... (next): Chapter $1$: Basic Concepts: Lesson $2 \text C$: Function of Two Independent Variables: Definition $2.68$ - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next): Entry:**region**