topological basis

Overview

Basis are usually an easier way to talk about a topology It gives us an easy way to compare topolgies

Definition

For a set X with a topology , a set of subsets of X (let it be ) is a basis for if

1. where Every element of X is covered by the basis
2. For 2 basis elements if then there is some basis element such that If x is in more than one basis, there is a third basis that is in the intersection (it is smaller than both of the original ones).