# Metric spaces

1. Feb 8, 2006

### Bob19

Hi

i have this following assignment in Analysis

Given $$X \subseteq \mathbb{R}^n$$ which is a nonempty subset of $$\mathbb{R}^n$$

The set $$\{ \| | x -y \| | \ | x \in X \}$$ has an infimum such that

$$f(y) = \{ \| | x -y \| | \ | x \in X \}$$

where $$f: \mathbb{R}^n \rightarrow \mathbb{R}^n$$

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

Regards,

Bob19

Last edited: Feb 8, 2006
2. Feb 8, 2006

### benorin

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)?

3. Feb 9, 2006

### matt grime

very similar to mathboy20s post in this subforum