For any subset A of a topological space X, we define the boundary of A to be JA =AnX\A.a) Show that int(A) and aA are disjoint and that A = int(A) U ĐAb) Show that aA=Ø if and only if A is open.

Answered: For any subset A of a topological space…

For any subset A of a topological space X, we define the boundary of A to be aA = AnX\A. a) Show that int(A) and aA are disjoint and that A = int(A) U ðA b) Show that JA=Ø if and only if A is open.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.2: Inner Product Spaces

Problem 94E

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For any subset A of a topological space X, we define the boundary of A to be JA =
AnX\A.
a) Show that int(A) and aA are disjoint and that A = int(A) U ĐA
b) Show that aA=Ø if and only if A is open.

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