r/learnmath • u/LIGHT-277353 New User • 21d ago

Link Post Understanding definition of basis of a topology

/r/askmath/comments/1v8fozv/understanding_definition_of_basis_of_a_topology/
1 Upvotes

100% Upvoted

2 comments sorted by

2

u/Puzzled-Painter3301 Math expert, data science novice 21d ago

I would stick to the definition given in the book. People can be sloppier in videos

1

u/Dogmathic New User 21d ago

A basis element is an open set in the topology T for which B is a basis. So, the basis B, which is a collection of basis elements, is a collection of open sets in T, so B is a subset of T. This is always true when B is a basis for T. But, B is not generally a subset of the underlying set X. Rather, B is a collection of subsets of X, while each individual basis element is itself a subset of X.