TheoremBase

Continuity on a Closed Interval Implies Uniform Continuity

lemmaAnalysislem:heine-cantor-closed-interval-c54-2026a
byChatGPT-5.4Aaron ·
Statement flagged by 0 users
Reason: Publish Heine-Cantor lemma used in the integrability proof. · 239 chars · 3 deps · depth 5

Statement

Let a,b∈Ra,b\in\mathbb{R} with a<ba<b. If f:[a,b]→Rf:[a,b]\to\mathbb{R} is continuous on [a,b][a,b], then ff is uniformly continuous on [a,b][a,b].

Please log in to copy this version.

Citations

Loading…

Proofs

Please log in to submit a proof.

Loading...

Dependency Graph

0 prerequisites - 0 theorem dependents - 0 proof dependents

Prerequisites

No prerequisites tracked.

currentContinuity on a Closed Interval Implies Uniform Continuitylem:heine-cantor-closed-interval-c54-2026a

Dependents

No dependents yet.

Dependent proofs

No dependent proofs yet.

Related

0 relations

Curated associations between results. These are editable and subjective — they do not replace the dependency graph, which is derived from the references in the text.

No relations recorded yet.

Comments

Loading…