My notes claim that the square root loop [tex] \sigma : S^1 \longrightarrow RP^1 ; z=\cos 2\pi t +i\sin 2\pi t \longrightarrow [\cos \pi t, \sin \pi t] [/tex] is a homeomorphism, where [x,y] is an equivalence class given by the antipodal equivalence relation on the circle. However, this map doesn't even seem to be a bijection. The proof simply says "by construction". Can anyone help?(adsbygoogle = window.adsbygoogle || []).push({});

**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!

# Square root loop

Loading...

Similar Threads - Square root loop | Date |
---|---|

A Square of the exterior derivative | Oct 19, 2016 |

Taylor expansion of the square of the distance function | Sep 28, 2015 |

Square of Gradient! | Sep 26, 2012 |

Squaring the Square -> Cubing the Rectangular Prism | Feb 20, 2012 |

Geometric construction of the square root | Jan 24, 2011 |

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