In general, if S is a connected set, can I conclude that S must be path connected?(adsbygoogle = window.adsbygoogle || []).push({});

Definition 1: S is connected if it is not disconnected. A set S is disconnected if it can be written as the union of two mutually separated sets, where mutually separated sets are two nonempty sets that do not contain any of each others boundary points.

Definition 2: S is path (or polygon) connected if any two points in S can be joined by a chain of line segments contain in S which abut (joined end to end), starting from one point and ending at the other.

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# Connected vs. Path Connected Sets

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