Let (X, d) be a metric space such that the intersection of open set and closed set is always open. Suppose that for each set E, there is a closed set F such that F⊂E. Show that if there is a set J ⊄ { Ø,X} such that J is open and closed, then there is a sequence of set {Jn} such thatJ1⊃J2⊃J3⊃...and Jn is open and closed, for all n∈N.

Let (X, d) be a metric space such that the intersection of open set and closed set is always open. Suppose that for each set E, there is a closed set F such that F⊂E. Show that if there is a set J ⊄ { Ø,X} such that J is open and closed, then there is a sequence of set {Jn} such thatJ1⊃J2⊃J3⊃...and Jn is open and closed, for all n∈N.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 18E: Let (A) be the power set of the nonempty set A, and let C denote a fixed subset of A. Define R on...

See similar textbooks