Let D be a domain and l be a closed line segment lying in D. In ele- mentary topology it is shown that l can be covered by a finite numbeir of open disks that lie in D and have their centers on l. Use this fact to prove that any two points of a domain D can be joined by a polygonal path in D having all its segments parallel to the coordinate axes.
Let D be a domain and l be a closed line segment lying in D. In ele- mentary topology it is shown that l can be covered by a finite numbeir of open disks that lie in D and have their centers on l. Use this fact to prove that any two points of a domain D can be joined by a polygonal path in D having all its segments parallel to the coordinate axes.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Transcribed Image Text:Let D be a domain and l be a closed line segment lying in D. In ele-
mentary topology it is shown that l can be covered by a finite numbeir
of open disks that lie in D and have their centers on l. Use this fact to
prove that any two points of a domain D can be joined by a polygonal
path in D having all its segments parallel to the coordinate axes.
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