so first let's take RP^2. I have a little trouble grasping why we can put a subspace topology on it. So RP^2 is the set of all lines through the origin in R^3. So if we take some subset S of RP^2 and the if set of points in R^3 which is the union of these lines in S is open then we can say we take the intersection of S and the open subset of R^3 and get a subspace topology. However, apparently you can only get the indiscrete topology? the reason i read for this was because the union would contain 0 but you can't have an open ball around 0. Let's say you take a single line as your subset S. you can't put an open ball around any of the points right? you won't necessarily have some delta in the x, y, z directions? how come the argument says you can't put an open ball around 0, but you can put it around the other points?(adsbygoogle = window.adsbygoogle || []).push({});

@_@

**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!

# RP^n as a topological space

Loading...

Similar Threads - RP^n topological space | Date |
---|---|

A Can I change topology of the physical system smoothly? | Oct 27, 2017 |

A Hyperbolic Coordinate Transformation in n-Sphere | May 24, 2017 |

I Do derivative operators act on the manifold or in R^n? | Jul 26, 2016 |

Maxwell's Equations in N Dimensions | Feb 22, 2016 |

N-sphere as manifold without embedding | Dec 29, 2015 |

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