View source for Discrete metric and topology/Metric space definition

Let {{M|X}} be a set. The ''discrete''<ref>Todo - this is how I was taught, can't find source</ref> metric, or ''trivial metric''<ref>Functional Analysis - George Bachman and Lawrence Narici</ref> is the [[Metric space|metric]] defined as follows:
* {{MM|d:X\times X\rightarrow \mathbb{R}_{\ge 0} }} with {{MM|1=d:(x,y)\mapsto\left\{\begin{array}{lr}0 & \text{if }x=y \\1 & \text{otherwise}\end{array}\right. }}
However any strictly positive value will do for the {{M|x\ne y}} case. For example we could define {{M|d}} as:
* {{MM|1=d:(x,y)\mapsto\left\{\begin{array}{lr}0 & \text{if }x=y \\v & \text{otherwise}\end{array}\right. }}
** Where {{M|v}} is some arbitrary member of {{M|\mathbb{R}_{> 0} }}<ref group="Note">Note the ''strictly greater than 0'' requirement for {{M|v}}</ref> - traditionally (as mentioned) {{M|1=v=1}} is used.
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==Notes==
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==References==
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{{Definition|Metric Space|Topology}}
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