Justify the examples(a) and (b) in details Definition: A topological space X is disconnected or separated if it is the unionof two disjoint, non-empty open sets. Such a pair A, B of subsets of X is called aseparation of X. A space X is connected provided that it is not disconnected. In otherwords, X is connected if there do not exist open subsets A and B of X such thatA + Ø, B+ Ø, ANB= Ø, AUB= X.%3DA subspace Y of X is connected provided that it is a connected space whenassigned the subspace topology. The terms connected set and connected subset aresometimes used to mean connected space and connected subspace, respectively. Еxample 5.1.1(a) A discrete space with more than one point is disconnected.(b) Any trivial space is connected since there fail to exist two non-emptyopen sets.

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Answered: (a) A discrete space with more than one…

(a) A discrete space with more than one point is disconnected. (b) Any trivial space is connected since there fail to exist two non-empty open sets.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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