Homework 6: Boundary of a Set, Subspace Topology

Instructions. Assignments should be stapled and written clearly and legibly.

1. Section 2.3, #2.24(f), 2.26(a)(c), 2.28(a).
2. Section 3.1, #3.4, 3.7, 3.11(b). Note that the latter two problems require proofs.
3. Let \(X\) be a topological space and \(A\subseteq X\). Prove that \(\partial A=\emptyset\) if and only if \(A\) is both open and closed.
4. True or False: If \(U\) is open, then \(U= \operatorname{Int}(\overline{U})\). Answer True or False, then justify your answer.