This is from Rudin, Functional Analysis 2.1. Not homework.(adsbygoogle = window.adsbygoogle || []).push({});

If X is an infinite-dimensional topological vector space which is the union of countably many finite-dimensional subspaces, prove X is first category in itself.

What about this example? Take R^n (standard n-dimensional space of reals) as each of the finite-dimensional subspaces. Then the union as n goes from 1 to infinity will be R^w.

R^w is infinite-dimensional, and it will contain closed sets that have non-empty interior. R^w seems like it will satify the axioms of the topological vector space. Hence this would contradict the problem.

What am I missing?

thanks

**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!

# Functional analysis question

Loading...

Similar Threads - Functional analysis question | Date |
---|---|

Question of "min" function from Spivak | Oct 10, 2014 |

Functional analysis convergence question | Apr 8, 2010 |

Another functional analysis question | Sep 24, 2007 |

A question on bounded linear operators (Functional Analysis) | Jun 7, 2007 |

Is this licitthen why?(functional analysis question) | Sep 23, 2006 |

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