# Usual Topology on Real

Usual Topology on $\mathbb{R}$

A collection of subsets of $\mathbb{R}$ which can be can be expressed as a union of open intervals forms a topology on $\mathbb{R}$, and is called topology on $\mathbb{R}$.

Remark:

Every open interval is an open set but the converse may not be true.

$A = \left\{ {x \in \mathbb{R}:2 < x < 3{\text{ or }}4 < x < 5} \right\}$

Usual Topology on ${\mathbb{R}^2}$

Consider the Cartesian plane ${\mathbb{R}^2}$, then the collection of subsets of ${\mathbb{R}^2}$ which can be expressed as a union of open discs or open rectangles with edges parallel to the coordinate axis from a topology, and is called a usual topology on ${\mathbb{R}^2}$.

Usual Topology on ${\mathbb{R}^3}$

Consider the Cartesian plane ${\mathbb{R}^3}$, then the collection of subsets of ${\mathbb{R}^3}$ which can be expressed as a union of open spheres or open cubed with edges parallel to coordinate axis from a topology, and is called a usual topology on ${\mathbb{R}^3}$.