Proposition 4.1.1. Let A CRm be open; let f: A → R", and let ECA. The following are true statements: 1. If f is Lipschitz on E, then f is uniformly continuous on E; 2. If f is locally Lipschitz, then f is continuous on A.
Proposition 4.1.1. Let A CRm be open; let f: A → R", and let ECA. The following are true statements: 1. If f is Lipschitz on E, then f is uniformly continuous on E; 2. If f is locally Lipschitz, then f is continuous on A.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.5: Graphs Of Functions
Problem 55E
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