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 B

_{1}and B

_{2}, then there is a basis element B

_{3}containing x such that B

_{3}[tex]\subset[/tex]B

_{1}[tex]\cap[/tex]B

_{2}.

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!