# Usual topology of the reals

## Definition

The "usual topology" or "standard topology" on the reals, [ilmath]\mathbb{R} [/ilmath] is the topology induced by the standard metric on the reals, which is the absolute value metric, [ilmath]d:\mathbb{R}\times\mathbb{R}\rightarrow\mathbb{R} [/ilmath] by [ilmath]d:(a,b)\mapsto \vert a-b\vert [/ilmath].

Said otherwise, given the metric space [ilmath](\mathbb{R},\vert\cdot\vert)[/ilmath] then the "standard topology of the reals" is the topology induced by this metric space

TODO: Anything to prove? This is a low priority page but check back at some point! Alec (talk) 15:19, 15 December 2017 (UTC)