# Usual Topology on Real

Usual Topology on $\mathbb{R}$:

A collection of subsets of $\mathbb{R}$ which can be can be expressed as 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.

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 union of open discs or open rectangles with edges parallel to coordinate axis from a topology, and is called 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 union of open spheres or open cubed with edges parallel to coordinate axis from a topology, and is called usual topology on ${\mathbb{R}^3}$.