Proposition 2.31 (Properties of Local Homeomorphisms). (a) Every homeomorphism is a local homeomorphism. (b) Every local homeomorphism is continuous and open. (c) Every bijective local homeomorphism is a homeomorphism.
Proposition 2.31 (Properties of Local Homeomorphisms). (a) Every homeomorphism is a local homeomorphism. (b) Every local homeomorphism is continuous and open. (c) Every bijective local homeomorphism is a homeomorphism.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Prove each statement is true
![Proposition 2.31 (Properties of Local Homeomorphisms).
(a) Every homeomorphism is a local homeomorphism.
(b) Every local homeomorphism is continuous and open.
(c) Every bijective local homeomorphism is a homeomorphism.
Exercise 2.32. Prove Proposition 2.31.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F86c8dcbb-d46d-4c91-a740-ef32ebf33ae0%2Fa9601a7a-6d8f-4513-a8c0-2cecf4d6c4a3%2Fllb9utr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Proposition 2.31 (Properties of Local Homeomorphisms).
(a) Every homeomorphism is a local homeomorphism.
(b) Every local homeomorphism is continuous and open.
(c) Every bijective local homeomorphism is a homeomorphism.
Exercise 2.32. Prove Proposition 2.31.
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