Hi(adsbygoogle = window.adsbygoogle || []).push({});

I have another question in the field of analysis.

[tex]Y \subseteq \mathbb{R}^n[/tex]

I'm suppose to show that if [tex]x \in \mathbb{R}^n[/tex], then the set

[tex]\{ || x - y || \ y \in Y \}[/tex]

has an infimum, such that

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

I know that I'm suppose to show that the infimum is the shortest distance between x and y. But how I proceed from there?

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

Sincerely Yours

Mathboy20

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# Infimum of a metric space

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