Open balls centered at infinity in the extended reals?

Question

Is an open ball of some radius $\delta >0$ defined at $+\infty$, if $+\infty$ is in the extended reals? (I have the same question for $-\infty$.)

Please explain how you define this open ball centered at $+\infty$ and also you mean "is the open ball a subset of the extended reals?" — user37238, Feb 11 '14 at 16:02

score 1 · Answer 1 · answered Feb 11 '14 at 15:54

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No, you would need to define a distance between $+\infty$ and the other points in order to define what an open ball of radius $\delta$ centered at $+\infty$ is.

answered Feb 11 '14 at 15:54

dani_s

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Are you sure? http://www.math.harvard.edu/~pflueger/math1b/limits.pdf – jack jacob Feb 11 '14 at 16:07
@jackjacob How would that contradict what I said? – dani_s Feb 11 '14 at 18:20

Open balls centered at infinity in the extended reals?

1 Answers1