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Is a Function Continuous in a Neighborhood If It's Continuous at a Point?

Context: Undergrad
Thread starter JG89
Start date Sep 14, 2009
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Continuity

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2 replies · 2K views

JG89

Thread starter
Sep 14, 2009

#1

If f is continuous at x = a, then is it continuous in some neighborhood of x = a as well?

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lurflurf

Homework Helper

Sep 14, 2009

#2

No
A standard example is
f(x)=x x rational
f(x)=0 x irrational

f is continuous at x=0

Elucidus

Sep 15, 2009

#3

lurflurf said:

No
A standard example is
f(x)=x x rational
f(x)=0 x irrational

f is continuous at x=0

And nowhere else. Not even very close to 0.

--Elucidus

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