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.

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter9: Multivariable Calculus
Section9.CR: Chapter 9 Review
Problem 3CR
icon
Related questions
Question
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.
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.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 1 steps

Blurred answer
Recommended textbooks for you
Calculus For The Life Sciences
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
College Algebra
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Elementary Geometry for College Students
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning