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According to definition 2.68, a set in the plane is called a region if it satisfies the following two conditions (p. 14):

1. "Each point of the set is the center of a circle whose entire interior consists of points of the set."

2. "Every two points of the set can be joined by a curve which consists entirely of points of the set."

I am having a hard time understanding the first condition. Can anyone provide an illustration in order to decipher the first condition meaning?

Thank you for help.