Exercise 3 1) Assume that X is a Hausdorff space. If D C X is a dense subset of X. If the point x D is an isolated point in D for the induced topology on the subset DC X, show that r is also an isolated point in X.
Exercise 3 1) Assume that X is a Hausdorff space. If D C X is a dense subset of X. If the point x D is an isolated point in D for the induced topology on the subset DC X, show that r is also an isolated point in X.
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.2: Vector Spaces
Problem 38E: Determine whether the set R2 with the operations (x1,y1)+(x2,y2)=(x1x2,y1y2) and c(x1,y1)=(cx1,cy1)...
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Exercise 3
Part 1
![Exercise 3
1) Assume that X is a Hausdorff space. If D C X is a dense subset of X. If
the point xD is an isolated point in D for the induced topology on the subset D C X, show that
x is also an isolated point in X.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa68164dd-6bba-4aa5-92bc-4824a71db092%2Fc2d6104d-ae18-47a6-9357-612208881213%2Faeubx0m_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Exercise 3
1) Assume that X is a Hausdorff space. If D C X is a dense subset of X. If
the point xD is an isolated point in D for the induced topology on the subset D C X, show that
x is also an isolated point in X.
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