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Suppose [tex]C\subseteq \mathbb{R}^{n}[/tex], if [tex]x \in \text{bd}\;C[/tex] where [tex]\text{bd}[/tex] denotes the boundary, a sequence [tex]\{x_{k}\}[/tex] can be found such that [tex]x_{k} \notin \text{cl}\;C[/tex] and [tex]\lim_{k\rightarrow \infty}x_{k} = x[/tex].

The existence of such sequence is guaranteed by the definition of boundary point, of which a neighborhood contains at least one point of [tex]C[/tex] and at least one point of [tex]\mathbb{R}^{n}\C[/tex]. (Explicit structure of the sequence is no longer our task...if you want, find it yourself...?)

Is my explanation right? Thanks.

Wayne

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# Boundary point

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