Introduction To Topology Mendelson Solutions Official

: Let F be a closed set. Suppose F is compact. Then F is closed and bounded. Conversely, suppose F is closed and bounded. Then F is compact.

: Let U and V be open sets. We need to show that U ∪ V is open. Let x ∈ U ∪ V. Then x ∈ U or x ∈ V. Suppose x ∈ U. Since U is open, there exists an open set W such that x ∈ W ⊆ U. Then W ⊆ U ∪ V, and hence U ∪ V is open. Introduction To Topology Mendelson Solutions

: Prove that the union of two open sets is open. : Let F be a closed set