(4) Q: Let ↑ denote the collection of the empty set and all subsets of R that contain the element 0. (a) Prove T is a topology on R. (b) Find the interior of the rational numbers, Q, as a subset of (R, 7). (c) Find the interior of (1, 5) as a subset of (R, 7). (d) Find the closure of [–1,2] as a subset of (R, 7). (c) Find the closure of (1,5) as a subset of (R, 7).

(4) Q: Let ↑ denote the collection of the empty set and all subsets of R that contain the element 0. (a) Prove T is a topology on R. (b) Find the interior of the rational numbers, Q, as a subset of (R, 7). (c) Find the interior of (1, 5) as a subset of (R, 7). (d) Find the closure of [–1,2] as a subset of (R, 7). (c) Find the closure of (1,5) as a subset of (R, 7).

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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