Definition:Region/Plane
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 It has been suggested that this page or section be merged into Definition:Open Region. Reason: This is defined in T&P just as "region" but it is clear from criterion $(1)$ that the region under discussion is definitely open. (Discuss) |
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