Topological Spaces
due by Monday, Aug 16, 2021
This assignment is based on material in lectures 1 and 2.

For sets
$A$
and$B$
, recall that$A\setminus B= \{a\in A: a \notin B\}$.
Which of the following always equals$A\setminus (A \setminus B)$?
Prove your answer.$A$
$B$
$A \cap B$
$A\cup B$

Let
$X=\{1, 2\}$
. What is the number of collections of subsets$\Omega\subset X$
that form a topology on$X$?
Prove your answer. 
Prove that the cofinite topology on a set
$X$
equals the discrete topology if and only if$X$
is finite.