# Dini’s theorem

If a monotonically increasing net $\{f_{n}\}$ of continuous real-valued functions on a topological space $(X,\tau)$ converges pointwise to a continuous function $f$, then the net converges to $f$ uniformly on compacts.

Title Dini’s theorem DinisTheorem 2013-03-22 12:20:32 2013-03-22 12:20:32 drini (3) drini (3) 4 drini (3) Theorem msc 54A20 TopologicalSpace Compact