Question

Give an example for sub basis topology and order topology being same

Answer 1

Answer:

Topological Basis. ... For the real numbers, the set of all open intervals is a basis. Stated another way, if is a set, a basis for a topology on is a collection of subsets of (called basis elements) satisfying the following properties.

• For each , there is at least one basis element containing .

Answer 2

Topological Basis. ... For the real numbers, the set of all open intervals is a basis. Stated another way, if is a set, a basis for a topology on is a collection of subsets of (called basis elements) satisfying the following properties. 1. For each , there is at least one basis element containing .