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Let $X$ be a nonempty convex subet of $A$. I need to Show that $z$ is an extreme point of $X$ if and only if the set $X − \{z\}$ is a convex set.

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    You probably mean $X - \{z\}$ at the end. Anyway: what have you tried and where are you stuck? Which direction is causing you difficulties? (and what's $A$?)2011-12-07
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    We do not vandalize questions here, Michael. Please don't do that again.2011-12-07
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    You could explain the reason why you deleted (again) the paragraph: *I first tried to show that if $z$ is an extreme point then $A − \{z\}$ us a convex set. I used the definition of a convex set, $\lambda x+(1-\lambda)y\;$ is in set $S$. I also attempted to go on the idea that $z=\lambda x_1+(1-\lambda)x_2$, so $x_1=x_2=z$.*2011-12-07

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