Exercise 1

Question

Let $d$ be the discrete metric on $\mathbb{K}$ and $X:=(\mathbb{K},d)$.\begin{enumerate}
\item[(a)] Give explicit descriptions of $\mathbb{B}_X(a,r)$ and $\bar{\mathbb{B}}_X(a,r)$ for $a\in X$ and $r>0$.
\item[(b)] Describe the cluster points of an arbitrary sequence in $X$.
\item[(c)] For $a\in X$, decribe all sequences $(x_n)$ in $X$ such that $x_n	o a$.
\end{enumerate}

Raoul · Accepted Answer

Let $a\in X$ and $r>0$, then we have three cases: if $01$, then $\mathbb{B}_X(a,r)=\bar{\mathbb{B}}_X(a,r)=X$, it should evident that $d(a,x)

Exercise 1

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Exercise 1

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