Prove that in R with the usual topology, the only open sets connected by paths are the open intervals. Please be as clear as possible, showing the steps and definitions if necessary. Thank you a lot.
Prove that in R with the usual topology, the only open sets connected by paths are the open intervals. Please be as clear as possible, showing the steps and definitions if necessary. Thank you a lot.
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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Prove that in R with the usual topology, the only open sets connected by paths are the open intervals.
Please be as clear as possible, showing the steps and definitions if necessary. Thank you a lot.
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