7. Assume that A is a subset of a metric space (X, d). Show that the interior points of A are the exterior points of AC, and that the exterior points of A are the interior points of AC. Check that the boundary points of A are the boundary points of Ac 8. Let (X, d) be a metric space, and let A be a subset of X. We shall consider A with the subset metric dA a) Assume that G C A is open in (X, d). Show that G is open in (A, dA) b) Find an example which shows that although G C A is open in (A, dA) it need not be open in (X, dx). c) Show that if A is an open set in (X, dx), then a subset G of A is open in (A, dA) if and only if it is open in (X, dx)

7. Assume that A is a subset of a metric space (X, d). Show that the interior points of A are the exterior points of AC, and that the exterior points of A are the interior points of AC. Check that the boundary points of A are the boundary points of Ac 8. Let (X, d) be a metric space, and let A be a subset of X. We shall consider A with the subset metric dA a) Assume that G C A is open in (X, d). Show that G is open in (A, dA) b) Find an example which shows that although G C A is open in (A, dA) it need not be open in (X, dx). c) Show that if A is an open set in (X, dx), then a subset G of A is open in (A, dA) if and only if it is open in (X, dx)

Name: Ans 7 only 7. Assume that A is a subset of a metric space (X, d). Show
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Description: Ans 7 only 7. Assume that A is a subset of a metric space (X, d). Show that the interior pointsof A are the exterior points of AC, and that the exterior points of A are the interiorpoints of AC. Check that the boundary points of A are the boundary po

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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Ans 7 only

7. Assume that A is a subset of a metric space (X, d). Show that the interior points
of A are the exterior points of AC, and that the exterior points of A are the interior
points of AC. Check that the boundary points of A are the boundary points of Ac
8. Let (X, d) be a metric space, and let A be a subset of X. We shall consider A with
the subset metric dA
a) Assume that G C A is open in (X, d). Show that G is open in (A, dA)
b) Find an example which shows that although G C A is open in (A, dA) it need
not be open in (X, dx).
c) Show that if A is an open set in (X, dx), then a subset G of A is open in (A, dA)
if and only if it is open in (X, dx)

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