The following question was part of my Topology assignment and I was unable to solve 2 parts out of 4.
Question:Let $X\times Y$ be topological spaces where $Y$ is Hausdorff. Let $X\times Y$ be the given product topology. Then for a function $f: X \to Y$ which of the following statements are true.
A If graph of $f$ is closed in $X\times Y$, then $f$ is continuous.
B If graph $f$ is closed in $X\times Y$, then $f$ need not be continuous.
I am unable to think how I can relate graph with continuity as graph is just a set in $X\times Y$.
I am not good in topology. So, your help is required.
Answer
Only B is correct.
Thank you.