\[ \text{Let X be a set, a topology on X is a family of sets } tau subseteq wp text{(X) (where} wp text{ is the power set) such that:} \]

\[ \begin{align} & (1) \emptyset , X \in \tau \\ & (2) \tau \text{ is closed under unions. For every } {A_{i}}_{i in I} subseteq \tau \text{ we have } \bigcup\limits_{i\in I} A_{i} \in \tau \\ & (3) \tau \text{ is closed under finite intersection. For every } A_{1},…,A_{n} \in \tau \text{ we have } A_{1} \cap …\cap A_{n} \end{align} \]

\[ \text{If } \tau \text{ is a topology on X we say that (X,}\tau \text{) is a topological space. The elements of }\tau \text{ are called open set} \]