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
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