Answered: Let X = R, and let T consist of 0, R,…

Let X = R, and let T consist of 0, R, and all intervals of the form (a, b) where a, b e R and a < b. Show that T is not a topology on IR. %3D

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter3: Groups

Section3.3: Subgroups

Problem 27E: (See Exercise 26) Let A be an infinite set, and let H be the set of all fS(A) such that f(x)=x for...

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Question

Prove that the first example is a topology and the second is not.

Let X = R, and let T consist of 0, R, and all intervals of the form (a, b) where a, b e R and
a < b. Show that T is not a topology on R.

Let X = N and let T consist of 0, N, and all sets An
{n, n + 1,n + 2, ...} where n >
1. Show that this is a topology on N.

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