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Let R be the set of real numbers equipped with the standard topology. Let A and B be two subsets of R defined respectively by A = { 1,1,2,4}, А B = (0, 1) U (1,2). Discuss each of the following questions with justification. (a) Is A open in R?

Let R be the set of real numbers equipped with the standard topology. Let A and B be two subsets of R defined respectively by A = { 1,1,2,4}, А B = (0, 1) U (1,2). Discuss each of the following questions with justification. (a) Is A open in R?

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.7: Relations
Problem 13E: 13. Consider the set of all nonempty subsets of . Determine whether the given relation on is...
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Let R be the set of real numbers equipped with the standard topology. Let A and B be two subsets of R defined respectively by A 1 = { 1, 1,2,4}, B = (0, 1) U (1,2). Discuss each of the following questions with justification. (a) Is A open in R? (b) Is B closed in R? (c) Is AUB closed in R?
Transcribed Image Text:Let R be the set of real numbers equipped with the standard topology. Let A and B be two subsets of R defined respectively by A 1 = { 1, 1,2,4}, B = (0, 1) U (1,2). Discuss each of the following questions with justification. (a) Is A open in R? (b) Is B closed in R? (c) Is AUB closed in R?
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