## A Topology Formed By Continuous Functions on [0,1]

Theorem

Letrepresent the set of all continuous functions onFor eachand define

The familyforms a basis for a topologyon

Proof

Suppose

Letand let

In fact ifthenandand

Therefore

Theorem

Letrepresent the set of all continuous functions onFor eachand define

The familyforms a basis for a topologyon

Proof

Suppose

Letand let

In fact ifthenandand

Therefore