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basis (topology)

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

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..' ?

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).

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