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Concept
Heine-Cantor Theorem
The
Heine-Cantor Theorem
states that if a function is continuous on a
compact metric space
, then it is uniformly continuous. This result is significant because it provides a
stronger form of continuity
that is applicable in many
areas of analysis
and topology, ensuring that
small changes in input
lead to
small changes in output
uniformly across the
entire space
.
Relevant Degrees
Mathematical Logic and Foundations 70%
Topology 30%
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