MathGloss
A
basis
for a
topology
τ
\tau
τ
on a set
X
X
X
is a collection
B
\mathcal B
B
of subsets of
X
X
X
such that
All points are contained in at least one element of
B
\mathcal B
B
, and
If
x
∈
B
’
∩
B
’’
x\in B’\cap B’’
x
∈
B
’
∩
B
’’
then there exists at least one
B
∈
B
B\in \mathcal B
B
∈
B
such that
x
∈
B
⊂
B
’
∩
B
’’
x\in B \subset B’\cap B’’
x
∈
B
⊂
B
’
∩
B
’’
.