Since things are a bit quiet here, I thought I would throw out a puzzle I came up with several years ago, after reading an article on connected sets:(adsbygoogle = window.adsbygoogle || []).push({});

Find two sets, P and Q, satisfying:

1) Both P and Q are completely contained in the (closed) rectangle in R^{2}with vertices at (1, 1), (1, -1), (-1, -1), and (-1, 1).

2) P contains the diametrically opposite points (1, 1) and (-1, -1) while Q contains(1, -1) and (-1, 1).

3) P and Q are both connected sets.

4) P and Q are disjoint.

The solution involves the difference between "connected" and "path-wise connected".

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

Dismiss Notice

Join Physics Forums Today!

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

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

# Connected Sets

Loading...

Similar Threads - Connected Sets | Date |
---|---|

Connected Set | Apr 6, 2011 |

Proof about connected sets | Jan 5, 2011 |

Connected sets in a topological space | May 28, 2009 |

An open connected set is path(polygon) connected | Feb 26, 2009 |

Connected sets | Oct 8, 2008 |

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