Topology

Let's get a more detailed overview of topology.

Bases

Similar to vector spaces, topological spaces can also have a basis.

note

AKA if you like it, put a basis on it

Again, topological space is some set $X$ with topology $\Tau$ defined on it.

And topology is a set of subsets of $X$.

For theoretical construction it is nice to just think of infinite families of subsets.

For example, we define compactness...