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
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ISBN:9781133382119
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Chapter3: Functions And Graphs
Section3.5: Graphs Of Functions
Problem 56E
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I need help proving the following two statements.
![Proposition 4.1.1. Let A C Rm 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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5870f95c-14fe-43b9-9aa2-c4d29aad7e05%2Ffbe8ff0f-19af-42e8-9cfa-136d3ecf190d%2Fc3lpaw_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Proposition 4.1.1. Let A C Rm 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.
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