Let X be an infinite set with the countable closed topology T={S subset of X; X-S is countable}. Then * None of the choices O (X,T) is not connected (X,T) is homeomorphic to (X,T1) where T1 is the finite closed topology on X O (X,T) is connected

Let X be an infinite set with the countable closed topology T={S subset of X; X-S is countable}. Then * None of the choices O (X,T) is not connected (X,T) is homeomorphic to (X,T1) where T1 is the finite closed topology on X O (X,T) is connected

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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Question

Let X be an infinite set with the
countable closed topology T={S subset
of X; X-S is countable}. Then *
None of the choices
O (X,T) is not connected
(X,T) is homeomorphic to (X,T1) where
T1 is the finite closed topology on X
O (X,T) is connected

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