Question

This is a review question for Intro to Topology

This is one question, multiple parts, so please answer them all as it's one question.

Be clear and concise with steps so I can follow, and please avoid cursive or quick writing as its hard to read.

Thank you!

(#5) Please answer and prove the questions below. Give an example of each as well after proving!!

(a) Prove that the union of open sets is open.

(b) Prove that the intersection of finitely many open sets is open.

(c) Prove that the intersection of any collection of closed sets is closed.

(d) Prove that the union of finitely many closed sets is closed.

Answer 1