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- Jan 27th 2008, 09:15 AMpatricia-donnellymetric space
Hello

- Jan 27th 2008, 01:16 PMThePerfectHacker
Suppose $\displaystyle x$ is an accumulation point of a set $\displaystyle A$. Then there exists

**distinct**$\displaystyle x_n \in A$ such that $\displaystyle x_n \to x$. Let $\displaystyle r>0$ then by definition of convergence it means $\displaystyle d(x,x_n) < r$ for $\displaystyle n\geq N$. Thus, $\displaystyle x_N,x_{N+1},...$ are**distinct**elements which lie in $\displaystyle B(x,r)$ and hence there are infinitely many.

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Using this, prove that any finite subset of X is closed.

- Jan 28th 2008, 08:34 AMpatricia-donnelly
You've been a great help. Thank you very much