Proposition 4.4.6. A subset A of a metric space S is closed if and only if A' C A. When we considered the set A = (0,1) in R, we observed that A' = [0, 1). Clearly A' is not contained in A, thus by Proposition 4.4.6, A = (0, 1) is not closed. For a, b €R with a
Proposition 4.4.6. A subset A of a metric space S is closed if and only if A' C A. When we considered the set A = (0,1) in R, we observed that A' = [0, 1). Clearly A' is not contained in A, thus by Proposition 4.4.6, A = (0, 1) is not closed. For a, b €R with a
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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