{X, Ø, {1}, {2},{1,2},{1,3}}, is (X, t) a connected a) Let X = {1,2,3} with the topology t= topological space? Justify your claim. b) Show that fis continuous if and only if for every C cY closed, the set f-1(C)c X is closed.

{X, Ø, {1}, {2},{1,2},{1,3}}, is (X, t) a connected a) Let X = {1,2,3} with the topology t= topological space? Justify your claim. b) Show that fis continuous if and only if for every C cY closed, the set f-1(C)c X is closed.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.CM: Cumulative Review

Problem 24CM

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a) Let X = {1,2,3} with the topology t= {X, Ø, {1}, {2},{1,2},{1,3}}, is (X, t) a connected
topological space? Justify your claim.
b) Show that f is continuous if and only if for every C c Y closed, the set f-1(C) c X is
closed.

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