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Answer by Arturo Magidin for $x\in \overline A \iff$ - how to derive...
Here are the definitions you are say you are using, once we dig through the comments (please put them in the post, this time and next!)For $\epsilon\gt0$ and a point $x$, $V_{\epsilon}(x) = \{y\mid...
View ArticleAnswer by student13 for $x\in \overline A \iff$ - how to derive definition of...
I'm assuming that with the limit definition you mean that $\overline A$ is the collection of points $a$ such that a path $\{x_i\}_{i = 1}^\infty \subseteq A$ exists that converges to $a$.The proof is...
View Article$x\in \overline A \iff$ - how to derive definition of closure
Let $X$ be a metric space with a metric $d$.Why does $x\in \overline A \iff \forall \epsilon>0, A\cap V_{\epsilon} (x) \neq \emptyset \tag{1}$?There are many posts that take it as...
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