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Problem 2. Give but not homeomorp

Problem 2. Give but not homeomorp

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Problem 2:** Give an example of sets \( S, T \subset \mathbb{R}^2 \) which are both contractible, but not homeomorphic. *Note on Terminology:* - *Contractible* means that each set can be continuously shrunk to a point within the space. - *Homeomorphic* means there is a continuous, bijective function with a continuous inverse between the two sets. This problem involves identifying examples in topology where two contractible sets are not homeomorphic. Consider how these properties allow flexibility in shape transformation while maintaining essential differences between the structures.
Transcribed Image Text:**Problem 2:** Give an example of sets \( S, T \subset \mathbb{R}^2 \) which are both contractible, but not homeomorphic. *Note on Terminology:* - *Contractible* means that each set can be continuously shrunk to a point within the space. - *Homeomorphic* means there is a continuous, bijective function with a continuous inverse between the two sets. This problem involves identifying examples in topology where two contractible sets are not homeomorphic. Consider how these properties allow flexibility in shape transformation while maintaining essential differences between the structures.
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