# Category:Definitions/Locally Uniform Convergence of Product

This category contains definitions related to Locally Uniform Convergence of Product.
Related results can be found in Category:Locally Uniform Convergence of Product.

Let $T = \struct {S, \tau}$ be a weakly locally compact topological space.

Let $\struct {\mathbb K, \norm {\, \cdot \,} }$ be a valued field.

Let $\sequence {f_n}$ be a sequence of locally bounded mappings $f_n: S \to \mathbb K$.

### Definition 1

The infinite product $\ds \prod_{n \mathop = 1}^\infty f_n$ converges locally uniformly if and only if every point of $T$ has a compact neighborhood on which it converges uniformly.

### Definition 2

The infinite product $\ds \prod_{n \mathop = 1}^\infty f_n$ converges locally uniformly if and only if it converges uniformly on every compact subspace of $T$.

## Pages in category "Definitions/Locally Uniform Convergence of Product"

The following 4 pages are in this category, out of 4 total.