topological space

\(\mathcal{T} \subseteq X\) is called a topology of \(X\) if:

1. \(\emptyset, X \in \mathcal{T}\)
2. \(A,B\in \mathcal{T} \Rightarrow A\cap B \in \mathcal{T}\)
3. For index set \(\mathcal{I}\), with \((A_{i})_{i\in \mathcal{I}}\), \(\bigcup_{i\in\mathcal{I}} A_i \in \mathcal{T}\)
4. note that a topology is closed under finite intersections and infinite unions

• superficially similar to Sigma Field – a measurable space. But there are key differences see here
• youtube video