So I'm reading about sets, and if A and B are combined, their commonalities are only counted once. This makes me think of sets as being one dimensional, i.e.:

1 2 3 4 5 6 7 8 9 10

A is (1,7). B is (5,10).

Are they one dimensional?

They demonstrate sets with circles, like a Ven diagram. This confuses me.

Is it like, a three dimensional graph with X, Y, and Z. X has a set of sets, Y has a set of sets, Z has a set of sets. Then you combine these all with a matrix?

I'm also fuzzy on the concept of a neighborhood.

Are there any specific mathematical concepts that are important to master to understand topology?