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.
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.1: Sets And Geometry
Problem 19E: What relationship subset, intersect, disjoint, or equivalent can be used to characterize the two...
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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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