### Topological Spaces

##### due by Thursday, Aug 18, 2022
1. Let $X=\{1, 2\}$. What is the number of collections of subsets $\Omega\subset 2^X$ that form a topology on $X$? Prove your answer.

2. Let $X=\Z$ and let $\Omega = \{V\subset \Z : \text{the set$\N\setminus V$is finite}\} \cup \{\phi\}$. Prove or disprove that $\Omega$ is a topology on $X$.