Usual topology of the reals

Definition

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

Said otherwise, given the metric space $(\mathbb{R},\vert\cdot\vert)$ 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