relative, or in the small (im kleinen), adj. (of some property of a topological space or of a function) holding only within some neighborhood of the given point rather than for all values. For example, a local maximum is a value of the function greater than any adjacent value, but it may not be the greatest value of the function over its whole range: for example, the curve shown below has a local maximum at A, but y is greater than this for x less than -2.5 or greater than 2. Compare global. See also locally compact, locally connected, locally Euclidean.
A is a local maximum.