Homework 1: Definition of a Topology

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

1. Section 1.1, #1.3, 1.5, 1.7.
2. Suppose that \(\ct_1\) and \(\ct_2\) are two topologies on a set \(X\). Prove that \(\ct_1\cap \ct_2\) is a topology on \(X\), but \(\ct_1\cup \ct_2\) need not be a topology on \(X\).