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