Suppose a space X has the intermediate value property (f: X->Y continuous, Y has the order topology), then X is connected.(adsbygoogle = window.adsbygoogle || []).push({});

How would you show this? This is just the converse of the intermediate value property.

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

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!

# How would you show that the intermediate value property implies connectedness?

Loading...

Similar Threads - show intermediate value | Date |
---|---|

I Derivative of a Real-Valued Function of Several Variables... | Feb 25, 2018 |

I Showing a step rigorously | Sep 29, 2017 |

I How to show that a 4-polytope is a tiling of the 3-sphere | Jul 1, 2017 |

...they say it's very difficult to show what sqrt2 is... | Jul 9, 2015 |

How do you show that if a(n) >= 0 for all n in N and a(n) = 0, then √a(n) Converges to 0 | Nov 5, 2014 |

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