This is a very simple question.... Because i'm not very good at these... notations... I feel like I need a clarification on what this means.. if X is a set, a basis for a topology on X is a collection [tex]B[/tex] of subsets of X (called basis elements) satisfying the following properties. 1. For each x[tex]\in[/tex]X, there is at least one basis element B containing x. 2. If belongs to the intersection of two basis elements B1 and B2, then there is a basis element B3 containing x such that B3[tex]\subset[/tex]B1[tex]\cap[/tex]B2. If B satisfies these two conditions, then we define the topology T generated by B as follows: A subset U of X is said to be open in X (That is, to be an element of T) if for each x[tex]\in[/tex]U, there is a basis element B [tex]\in[/tex] [tex]B[/tex] and B[tex]\subset[/tex]U. Note that each basis element is itself an element of T. okay... i know what basis topology is... by reading all of these.. but i want a clarification on what this... U is... is it the whole set? like the Union? or what? or is it just a variable that they define? I just want a clarification.. Thank you!