# basis (topology)

## Primary tabs

Keywords:
topology
Synonym:
basis, base, topology generated by a basis
Type of Math Object:
Definition
Major Section:
Reference
Groups audience:

## Mathematics Subject Classification

54A99 no label found

## Comments

### V ?

Line 2: 'Equivalently, B is a basis if and only if whenever U is open and x is an element of U then there is an open set V such that x is an element of V is a subset of U.'

What is the relationship between V and B? Should it be 'there is an open set V which is an element of B such that..' ?

### about proposition 1

there is at least one condition missing, since even the empty set fullfills the conditions of proposition 1. But a basis must have one element, (if X ist not empty).