Hey guys, doin another rudin-related question. Here Goes:(adsbygoogle = window.adsbygoogle || []).push({});

Show that if E [tex]\subseteq[/tex] [tex]\Re[/tex] is open, then E can be written as an at most countable union of disjoint open intervals, i.e., E=[tex]\bigcup[/tex]_{n}(a_{n},b_{n}). (It's possible that a_{n}=-[tex]\infty[/tex] b_{n}=+[tex]\infty[/tex] for some n.)

My attempt:

Take the set of all Neighborhoods of all of the rationals of a rational radius inRto beA. Now all members of E intersect A make up E. Take the union of all of the neighborhoods in this set E intersect A and this is a countable union of disjoint sets.

Is there a problem with this?

**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!

# Real analysis

Loading...

Similar Threads - Real analysis | Date |
---|---|

I Proof that lattice points can't form an equilateral triangle | Feb 8, 2017 |

Calculus Derivations | Feb 17, 2016 |

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

A question on the paragraph before 7.23 of Rudin's Real and complex analysis | Mar 2, 2012 |

Radius of convergence: 1/(1+x^2) about 1, using only real analysis | Nov 28, 2011 |

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