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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 ??

Regards,

Bob19

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# Homework Help: Metric spaces

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