# Linear function: relation between linearity and continuity

Given a linear function $A$ between two normed Vectorspaces i have to show euquality of the follwing statements:

1. $A$ is continuous
2. There exists a point where $A$ is continuous
3. $A$ is Lipschitz-continuous

$3\to1\to2 \:$ is obviously true, but i can't find any other relation.