Usual topology of the reals

From Maths
Jump to: navigation, search

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)


References

(Unknown grade)
This page requires references, it is on a to-do list for being expanded with them.
Please note that this does not mean the content is unreliable, it just means that the author of the page doesn't have a book to hand, or remember the book to find it, which would have been a suitable reference.
The message provided is:
Topology