Introduction To Topology Mendelson Solutions Here

Let $X$ be a topological space and let $f: X \to Y$ be a continuous function. Prove that if $X$ is compact, then $f(X)$ is compact.

Let $X$ be a metric space and let $A \subseteq X$. Prove that $A$ is open if and only if $A = \bigcup_{a \in A} B(a, r_a)$ for some $r_a > 0$. Introduction To Topology Mendelson Solutions

Let $A \subseteq X$. Suppose that $A$ is open. Then, for each $a \in A$, there exists $r_a > 0$ such that $B(a, r_a) \subseteq A$. This implies that $A = \bigcup_{a \in A} B(a, r_a)$. Let $X$ be a topological space and let