Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Functional analysis

  1. Jan 27, 2008 #1
    Hello

    I need help with an analysis proof and I was hoping someone might help me with it. The question is:

    Let (X,d) be a metric space and say A is a subset of X. If x is an accumulation point of A, prove that every r-neighbourhood of x actually contains an infinite number of distinct points of A (where r>0). Using this, prove that any finite subset of X is closed.

    Any help or suggestions would really be appreciated.
    Thanks
     
  2. jcsd
  3. Jan 27, 2008 #2

    jambaugh

    User Avatar
    Science Advisor
    Gold Member

    To get started you'll need to carefully parse the definitions. Closure means all Cauchy sequences converge within the set. How will this apply to a finite set? Can't you show that there is a minimum distance among the points? How will that relate to the definition of a Cauchy sequence?

    I think you're missing an assumption in the first part. Let A be a set of only one point and x be that point. Was A supposed to be a non-empty open subset?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Functional analysis
  1. Functional analysis (Replies: 5)

Loading...