ABSTRACT
This chapter introduces a stronger version of continuity, called uniform continuity, which attempts to address these limitations. It shows that that any function that satisfies this new definition will automatically satisfy our old definition, but that the converse of this statement is not true. There is a difference between continuity and uniform continuity: uniform continuity implies continuity but the converse is not true in general. It is natural to ask whether there are specific additional conditions under which continuity implies uniform continuity.
