Let X be a normed space.Show that the function f:X to Real numbers defined by f(x)=norm x is continuous on X.

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- Oct 16th 2012, 08:00 AMchathtopology
Let X be a normed space.Show that the function f:X to Real numbers defined by f(x)=norm x is continuous on X.

- Oct 21st 2012, 01:59 AMgirdavRe: topology
Use $\displaystyle |\lVert x\rVert-\lVert y\rVert|\leq \lVert x-y\rVert$.