1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Rudin Chapter 2 Problem 25

  1. Jul 5, 2012 #1
    Rudin's problem asks: Prove that every compact metric space K has a countable base.

    My concern is how valid this statement really is. Wouldn't a finite compact metric space be unable to have a countable base?
  2. jcsd
  3. Jul 5, 2012 #2
    Rudin probably defines countable as either finite or in bijection with [itex]\mathbb{N}[/itex]. So finite things are countable to him.

    You should look up his definition to be sure.
  4. Jul 5, 2012 #3
    Rudin distinguishes finite sets and countable sets in his book. Would this affect the validity of the statement?
  5. Jul 5, 2012 #4
    Yes, it does. You want the base to be either finite or countable.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook