Answered: (a) Prove or disprove: If SC Xis a… | bartleby

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.3: Lines

Problem 10E

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Question 7

(a) Prove or disprove: If S C Xis a compact subset of a metric spaceX,p>, then S is
closed and bounded.
(b) True or false? Justify your answer: A closed, bounded subset SC X of a metric space
<X,p>, is compact.
(c) Given the set T := {(x, y) € R²: |ay| < 1}. Is T a compact set? Show your working. If
you say it is not compact, then find the smallest compact set containing T.
2
(d) Given a metric spaceX, p>, and two compact subsets S, TE X. Prove that SUT is
compact.

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