Let X and Y be two discrete spaces, then * X is never homeomorphic to Y X is homomorphic to Y if and only if X and Y are both infinite X is homeomorphic to Y if and only if X and Y have the same cardinality X is homeomorphic to Y if and only if X and Y are both finite

Let X and Y be two discrete spaces, then * X is never homeomorphic to Y X is homomorphic to Y if and only if X and Y are both infinite X is homeomorphic to Y if and only if X and Y have the same cardinality X is homeomorphic to Y if and only if X and Y are both finite

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 and Y be two discrete spaces,
then *
X is never homeomorphic to Y
X is homomorphic to Y if and only if X
and Y are both infinite
X is homeomorphic to Y if and only if
X and Y have the same cardinality
X is homeomorphic to Y if and only if
X and Y are both finite

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