Let A, B be two subsets of R and: A+B:={ x+y : x E A, y E B}. A. Show that if A or B are open then A+B is open . B. Using sequences, Show that if A and B are compact then A+B is compact. C. Show that if A and B are closed A+B does not imply that A + B is.
Let A, B be two subsets of R and: A+B:={ x+y : x E A, y E B}. A. Show that if A or B are open then A+B is open . B. Using sequences, Show that if A and B are compact then A+B is compact. C. Show that if A and B are closed A+B does not imply that A + B is.
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.2: Vector Spaces
Problem 48E: Let R be the set of all infinite sequences of real numbers, with the operations...
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Let A, B be two subsets of R and:
A+B:={ x+y : x E A, y E B}.
A. Show that if A or B are open then A+B is open .
B. Using sequences, Show that if A and B are compact then A+B is compact.
C. Show that if A and B are closed A+B does not imply that A + B is.
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