(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

[tex]\underline{x} [/tex] point in [tex] R^{n} A \subset R^{n}[/tex]

the distanse between [tex] \underline{x}[/tex] to A is definde as [tex] d(\underline{x},A) = \left\{ inf{||\underline{x} = \underline{a}|| | a \in A \right\}[/tex]

A,B are closed Disjoint sets in R^{n} we define [tex]f(\underline{x}) = \frac{d(\underline{x},B)}{d(\underline{x},A) + d(\underline{x},B)}[/tex]

to each [tex]\underline{x} \subset R^{n}[/tex] and [tex]\underline{y} \subset R^{n} [/tex] [tex]

|d(\underline{x},A)-d(\underline{y},A)| \leq||\underline{x}-\underline{y}||[/tex]

Prove that [tex]f(\underline{x})[/tex] Continuous

2. Relevant equations

everything in calculus

3. The attempt at a solution

Well I've tried with Cauchy test for limits of function but this does not give me a Continuous function..

from there I am A bit stuck.

Thank you.

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# Homework Help: D(x,A) = inf{||x-a|| | a=A}

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