This is probably a stupid question.. but 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 B1 and B2, then there is a basis element B3 containing x such that B3[tex]\subset[/tex] B1[tex]\cap[/tex]B2. 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!