Given a set $X$, define a function $d:X\times X\rightarrow \mathbb{R}$ by $d(x,y) = 1$ if $x\neq y$ and $d(x,y)=0$ if $x=y$. Show that the metric topology on $X$ is equal to the discrete topology.
Discrete and metric topologies equivalence
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general-topology
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1What a discrete hint! – 2011-04-30
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0The title does not reflect the question. – 2011-04-30