# 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 $${\mathbb{R}^3}$$.