# Compactness of a space

1. Aug 18, 2009

### symv

I am considering the set of all bounded signals given by

$$X = \left\{ x:\ |x(t)| \leq X_{\max}, \forall t \right\}.$$

Is this set compact? Can anyone help me?

Thank you guys

2. Aug 19, 2009

### Reb

No, bounded alone does not imply compact
(in the topology of uniform convergence).

3. Aug 19, 2009

### g_edgar

in what topology, in what space of functions ?

4. Aug 19, 2009

### Reb

He said signals, so I guess it's something like periodic functions
that are a.e. C^1.