- #1

tomboi03

- 77

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Can someone tell me the difference between subbasis and basis.. in topology?? I know the definitions...

So Subbasis is defined to be the collection T of all unions of finite intersections of elements of S (subbasis)

sooo... S is pretty much a topology on X which is a collection of subsets of X whose union equals X.

Basis, however... is

If X is a set, basis on X is a collection B of subsets of X (basis elements) s.t.

1. for each x [tex]\in[/tex] X, there is at least one basis element B containing x.

2. If x 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}.

Right? So pretty much... A subset U of X is said to be open in X if for each x [tex]\in[/tex] U, there is a basis element B [tex]\in[/tex] [tex]B[/tex] such that x [tex]\in[/tex] B and B [tex]\subset[/tex] U.

But I'm still not understanding this quite... so well..

Can someone explain this to me??

Thank You!