my question is about: show that if $\kappa > 2^\omega$, then the space $2^\kappa$ is not seperable. (kunen, page 86, exercise 4) – ıf there exist a countable dense set $D$ where is the contradiction? since density of $D$ not clear for me in product space $2^\kappa$, I could not say anything about contradiction.
kunen exercise about ccc which is not separable
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set-theory
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2The book gives a hint: "if $D \subset {}^\kappa 2$ is countable, show that there are $\alpha < \beta$ such that $(\forall f \in D)(f(\alpha) = f(\beta))$". This is enough to show that $D$ is not dense, because we can look at the open set all of whose elements are $1$ on $\alpha$ and $0$ on $\beta$, and $D$ does not meet this set. – 2011-06-11