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Isomorphisms and path classes

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(See attached file for full problem description with proper symbols)

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a) Under what conditions will two path classes, and , from to , give rise to the same isomorphism of onto ?

b) Let be an arcwise-connected space. Under what conditions is the following true:

For any two points , all path classes from to give rise to the same isomorphism of onto ?

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Solution Summary

This answers to questions about conditions necessary for path classes to give rise to a given isomorphism.

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