Help ASAP (a) Prove that every nonempty proper subset of a connected space has anonempty boundary. Is the converse also true?(b) Let X be a connected metric space with an unbounded metric d. Prove thatthe set {y | d(x, y) = r} is nonempty for each .x e X. Is this also true whenX is disconnected?

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(a) Prove that every nonempty proper subset of a connected space has a nonempty boundary. Is the converse also true?

Elementary Linear Algebra (MindTap Course List)

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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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Help ASAP

(a) Prove that every nonempty proper subset of a connected space has a
nonempty boundary. Is the converse also true?
(b) Let X be a connected metric space with an unbounded metric d. Prove that
the set {y | d(x, y) = r} is nonempty for each .x e X. Is this also true when
X is disconnected?

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