Dini’s theorem

If a monotonically increasing net {fn} of continuousMathworldPlanetmathPlanetmath real-valued functions on a topological spaceMathworldPlanetmath (X,τ) convergesPlanetmathPlanetmath pointwisePlanetmathPlanetmath to a continuous function f, then the net converges to f uniformly on compactsPlanetmathPlanetmath.

Title Dini’s theorem
Canonical name DinisTheorem
Date of creation 2013-03-22 12:20:32
Last modified on 2013-03-22 12:20:32
Owner drini (3)
Last modified by drini (3)
Numerical id 4
Author drini (3)
Entry type Theorem
Classification msc 54A20
Related topic TopologicalSpace
Related topic Compact