A map

*
from a metric an are
*
to a metric room
*
is stated to it is in uniformly continuous if because that every
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0" />, there exists a
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0" /> such the
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Examples that uniformly consistent functions encompass Lipschitz functions and also those solve the Hölder condition. Note yet that not all consistent functions space uniformly consistent with two very straightforward counterexamples being

*
(for
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) and
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(for
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. Top top the other hand, every duty which is constant on a compact domain is have to uniformly continuous.

You are watching: Uniformly continuous vs continuous


SEE ALSO: consistent Function,Equicontinuous

This entry contributed by ChristopherStover


REFERENCES:

Carothers, N.L. RealAnalysis. Brand-new York: Cambridge college Press, 2000.


CITE THIS AS:

Stover, Christopher. "Uniformly Continuous." from couchsurfingcook.com--A couchsurfingcook.com net Resource, produced by Eric W. Weisstein. Https://couchsurfingcook.com/UniformlyContinuous.html


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