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Homework Help: Metric spaces

  1. Feb 8, 2006 #1

    i have this following assignment in Analysis

    Given [tex]X \subseteq \mathbb{R}^n[/tex] which is a nonempty subset of [tex]\mathbb{R}^n[/tex]

    The set [tex]\{ \| | x -y \| | \ | x \in X \}[/tex] has an infimum such that

    [tex]f(y) = \{ \| | x -y \| | \ | x \in X \}[/tex]

    where [tex]f: \mathbb{R}^n \rightarrow \mathbb{R}^n [/tex]

    I need a hint on howto show that if [tex]y \in X[/tex] then f(y) = 0 ??


    Last edited: Feb 8, 2006
  2. jcsd
  3. Feb 8, 2006 #2


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    Fix x in X. What is the shortest distance between x and y if y is allowed to be in X (note that x is in X)?
  4. Feb 9, 2006 #3

    matt grime

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    very similar to mathboy20s post in this subforum
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