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The '''Uniform Continuity Theorem''' states:
The '''Uniform Continuity Theorem''' states:
<blockquote>
<blockquote>
If ''f'' is a continuous function, and the domain of ''f'' is a [[compact space]], then ''f'' is uniformly continuous.
If ''f'' is a [[continuous]] function, and the domain of ''f'' is a [[compact space]], then ''f'' is [[uniform continuity|uniformly continuous]]
</blockquote>
</blockquote>
[[category:mathematics]]
[[Category:Topology]]