Topological space

Set $A$ with a family $\mathcal{A}$ of its subsets is called topological space, if
the following conditions are satisfied:

• $\emptyset \in \mathcal{A}$, $A \in \mathcal{A}$
• $\forall \, X_1,X_2 \in \mathcal{A} \colon X_1 \cap X_2 \in \mathcal{A}$
• $\forall \, \{X_\alpha\} \subset \mathcal{A} \colon \bigcup_\alpha X_\alpha \in \mathcal{A}$