Category:Uniform Convergence
Jump to navigation
Jump to search
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 31 pages are in this category, out of 31 total.
C
D
F
L
U
- Uniform Limit of Analytic Functions is Analytic
- Uniform Limit of Holomorphic Functions is Holomorphic
- Uniform Product of Continuous Functions is Continuous
- Uniformly Absolutely Convergent Product is Uniformly Convergent
- Uniformly Continuous Function Preserves Uniform Convergence
- Uniformly Convergent iff Difference Under Supremum Metric Vanishes
- Uniformly Convergent Product Satisfies Uniform Cauchy Criterion
- Uniformly Convergent Sequence Evaluated on Convergent Sequence
- Uniformly Convergent Sequence Multiplied with Function
- Uniformly Convergent Sequence Multiplied with Function/Corollary
- Uniformly Convergent Sequence of Continuous Functions Converges to Continuous Function
- Uniformly Convergent Sequence of Continuous Functions Converges to Continuous Function/Corollary
- Uniformly Convergent Sequence on Dense Subset
- Uniformly Convergent Series of Continuous Functions Converges to Continuous Function
- Uniformly Convergent Series of Continuous Functions Converges to Continuous Function/Corollary