Define a \[\textit{base}\] for a topology on a set \(X\)

Given a sequence of points in a topological space \(X\), define
\[\textit{convergence to the point } x\in X\]

Given two topologies \(\mathcal{T}_1,\mathcal{T}_2\), define \[\textit{coarser/finer}\]

Give a definition of a topology on a set \(X\) in terms of open sets. Define \(\textit{topological space}\)

Define a \(\textit{metric}\) (distance function) on a set \(X\)