Category:Uniform Convergence

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This category contains results about Uniform Convergence.
Definitions specific to this category can be found in Definitions/Uniform Convergence.


Let $S$ be a set.

Let $M = \struct {A, d}$ be a metric space.

Let $\sequence {f_n}$ be a sequence of mappings $f_n: S \to A$.

Let:

$\forall \epsilon \in \R_{>0}: \exists N \in \R: \forall n \ge N, \forall x \in S: \map d {\map {f_n} x, \map f x} < \epsilon$


Then $\sequence {f_n}$ converges to $f$ uniformly on $S$ as $n \to \infty$.

Subcategories

This category has the following 3 subcategories, out of 3 total.

Pages in category "Uniform Convergence"

The following 29 pages are in this category, out of 29 total.