Definition:Region/Plane

It has been suggested that this page or section be merged into Definition:Open Region. In particular: This is defined in T&P just as "region" but it is clear from criterion $(1)$ that the region under discussion is definitely open. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{Mergeto}} from the code.

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): region