A component E of a topological space X is a maximal connected subset of X.Clearly, E + 0, E is connected, and E is not a proper subset of any other connectedsubset of X.(a) Consider the following topology of X = {a, b, c, d, e}:T = {X,Ø, {a}, {c, d}, {a, c, d}, {b, c, d, e}}.What are the components of X?(b) Show that every component E of X is closed.

In topology and related branches of mathematics, a connected space is a topological space that…

Answered: (a) Consider the following topology of…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.2: Mappings

Problem 22E

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(a) Consider the following topology of X = {a,b, c, d, e}: T = {X, 0, {a}, {c, d}, {a, c, d}, {b, c, d, e}}. What are the components of X? (b) Show that every component E of X is closed.