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Everything about Uniform continuity
Uniform restraint of the change in functions
In mathematics, a real function of real numbers is said to be uniformly continuous if there is a positive real number such that function values over any function domain interval of the size are as close to each other as we want. In other words, for a uniformly continuous real function of real numbers, if we want function value differences to be less than any positive real number, then there is a positive real number such that for any and in any interval of length within the domain of. Wikipedia →
🧠Start here: a 6-step reading path
- Read the overview: Uniform continuityA 5-minute orientation
- Skim a recent paper: From Classical to Quantum: Uniform Continuity Bounds on Entropies in Infinite DimensionsInfluential work since 2022
- Pick up a classic book: Topics in Banach spaces of continuous functionsThe most-reprinted book on the subject
- Read the landmark paper: Continuous state feedback guaranteeing uniform ultimate boundedness for uncertain dynamic systemsCited 1,363 times
- Go sideways: Continuous functionA closely related topic
- Go sideways: Arzelà –Ascoli theoremA closely related topic
đź“– Definitions
Noun The property of being uniformly continuous.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Continuous state feedback guaranteeing uniform ultimate boundedness for uncertain dynamic systems
Uniform-sense normal simple shear of the continental lithosphere
Pseudocompactness and uniform continuity in topological groups
Strong uniform continuity
Continuity of pullback and uniform attractors
Uniform Continuity of Continuous Functions on Uniform Spaces
Uniform Continuity, Uniform Convergence, and Shields
Uniform continuity and compactness in topological groups
🆕 Influential since 2022
From Classical to Quantum: Uniform Continuity Bounds on Entropies in Infinite Dimensions
Zero-r Law on the Analyticity and the Uniform Continuity of Fractional Resolvent Families
Exact Uniform Modulus of Continuity and Chung’s LIL for the Generalized Fractional Brownian Motion
A Tight Uniform Continuity Bound for the Arimoto-RĂ©nyi Conditional Entropy and its Extension to Classical-Quantum States
Uniform continuity bound for sandwiched RĂ©nyi conditional entropy
đź“š Books worth reading
- 📕Topics in Banach spaces of continuous functionsA. J. Ellis · 1978
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
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