- #1

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Construct a compact set of real numbers whose limit points form a

countable set.

countable set.

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- Thread starter forget_f1
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- #1

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Construct a compact set of real numbers whose limit points form a

countable set.

countable set.

- #2

arildno

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Shouldn't a single point be enough?

- #3

arildno

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I may have forgotten the precise definition of "the limit point".

You might instead look at a convergent sequence in R; that is a compact set, with one limit point.

- #4

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- #5

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a limit point of a set A is a point p such that for any neighborhood of p

(ie Ball(p,r) , where p is the origin and r=radius can take any value >0)

there exists a q≠p where q belongs in B(p,r) and q belongs to A.

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matt grime

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- #7

arildno

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Yeah, I kind of remembered that a bit late...forget_f1 said:

a limit point of a set A is a point p such that for any neighborhood of p

(ie Ball(p,r) , where p is the origin and r=radius can take any value >0)

there exists a q≠p where q belongs in B(p,r) and q belongs to A.

Finite sets are countable.

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- #8

HallsofIvy

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arildno said:Yeah, I kind of remembered that a bit late...

Finite sets are countable.

But the original post probably

- #9

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Since the set is closed and bouned then it is compact. (theorem)

Or

It can prove by definition that A is compact, which is what I did since I forgot to use the theorem above which would have made life easier :)

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