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creative_

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creative_

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mathwonk

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creative_

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Hi mathwonk,

I mean Hausdorff space.

I mean Hausdorff space.

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Proof: Let K be a compact neighborhood of 0. We can assume that K is balanced. Since (1/2)K is a neighborhood of 0, there are finitely many points x

[tex]K\subseteq (x_1+\frac{1}{2}K)\cup...\cup (x_n+\frac{1}{2}K)[/tex]

Let M be the finite dimensional subspace spanned by the x

K is balanced, so [itex]E=\bigcup_n 2^n K[/itex]. Thus [itex]\varphi(E)=\varphi(K)[/itex]. Thus E/M is compact. Which implies that E/M is one point. Thus E=M.

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mathwonk

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what do you mean by zero in a topological space? oh i see micromass, you assumed he meant a vector space. the argument you gave is a variation of the argument for Riesz's theorem that I referred to. That's a nice example of extending an argument to a more general setting. I didn't know that version.

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creative_

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Thank you micromass. Your proof makes sense.

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