Let X and Y be metric spaces. A family F of functions from X to Y is said to be equibounded if there exists a boundedPlanetmathPlanetmathPlanetmath subset B of Y such that for all fF and all xX it holds f(x)B.

Notice that if F𝒞b(X,Y) (continuous bounded functions) then F is equibounded if and only if F is bounded (with respect to the metric of uniform convergenceMathworldPlanetmath).

Title equibounded
Canonical name Equibounded
Date of creation 2013-03-22 13:16:55
Last modified on 2013-03-22 13:16:55
Owner paolini (1187)
Last modified by paolini (1187)
Numerical id 5
Author paolini (1187)
Entry type Definition
Classification msc 54E35
Synonym equi bounded
Synonym equi-bounded