Topic summary
Local minimum
Extracted from the Wikipedia article Maximum and minimum.
Definition
If the domain X is a metric space, then f is said to have a local (or relative) maximum point at the point x, if there exists some ε > 0 such that f(x) ≥ f(x) for all x in X within distance ε of x. Similarly, the function has a local minimum point at x, if f(x) ≤ f(x) for all x in X within distance ε of x. A similar definition can be used when X is a topological space, since the definition just given can be rephrased in terms of neighbourhoods. Mathematically, the given definition is written as follows: