0.1 Open Sets & Closed Sets on Metric Spaces
The concept of open and closed sets is important
For [[knowledge-mathematics-analysis-functional-analysis-metric-spaces|metric space]] \((X,d)\) a subset \(A\subseteq X\) is said to be open if for each \(x\in A\) there exists an open epsilon ball such that \(B_\epsilon(x)\subseteq A\). A subset \(A\subseteq X\) is said to be closed if its complement \(A^c\) is open.