N*******e
发帖数: 10 | 1 If f: [a, b] -> R and if the graph G(f) = {(x, f(x)): x in [a, b]} is
connected. Does it follow that f is continuous? How to prove the conclusion?
Many Thanks! | B****n
发帖数: 11290 | 2 Consider
f(x)=sin(1/x) when x is in (0,1]
=0 when x is 0
{(x,f(x)): x in [0,1]} is connected in R^2, but f(x) is not continuous at 0.
conclusion?
【在 N*******e 的大作中提到】
: If f: [a, b] -> R and if the graph G(f) = {(x, f(x)): x in [a, b]} is
: connected. Does it follow that f is continuous? How to prove the conclusion?
: Many Thanks!
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