O N 93%2:47Let X and Y be two discrete spaces,then *X is homomorphic to Y if and only ifX and Y are both infiniteX is homeomorphic to Y if and onlyif X and Y are both finiteX is never homeomorphic to YX is homeomorphic to Y if and onlyif X and Y have the same cardinalityWhich one of the followingstatements is true? *R with the Euclidean topology and Rwith the finite closed topology arenot homeomorphicNone of the choicesR with the Euclidean topology and Rwith the finite closed topology arehomeomorphicR with the Euclidean topology and Rwith the discrete topology arehomeomorphic

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Let X and Y be two discrete spaces, then *

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.2: Vector Spaces

Problem 48E: Let R be the set of all infinite sequences of real numbers, with the operations...

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Question

O N 93%
2:47
Let X and Y be two discrete spaces,
then *
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 are both finite
X is never homeomorphic to Y
X is homeomorphic to Y if and only
if X and Y have the same cardinality
Which one of the following
statements is true? *
R with the Euclidean topology and R
with the finite closed topology are
not homeomorphic
None of the choices
R with the Euclidean topology and R
with the finite closed topology are
homeomorphic
R with the Euclidean topology and R
with the discrete topology are
homeomorphic

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