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.

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Connected vs. Path Connected Sets

Loading...

Similar Threads - Connected Path Connected | Date |
---|---|

I Connections on principal bundles | Jan 22, 2018 |

Path connected subgroups of SO(3), please help | Jul 29, 2014 |

A path connected product of path connected spaces | Oct 16, 2010 |

R^2 - A, with A being a countable set, path-connected? | Feb 16, 2010 |

Path connected and connected. | Feb 5, 2008 |

**Physics Forums - The Fusion of Science and Community**