Usual topology wikipedia
Usual Topology on RealUsual 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 $${\mathbb{R}^3}$$. |