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ii) Endow R with its order topology. Is it true that if A CR has no minimum and maximum, then the order topology on A agrees with its subspace topology TA? Justify your answer.

ii) Endow R with its order topology. Is it true that if A CR has no minimum and maximum, then the order topology on A agrees with its subspace topology TA? Justify your answer.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.5: Subspaces, Basis, Dimension, And Rank
Problem 10EQ
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(ii) Endow R with its order topology. Is it true that if A C R has no minimum and maximum, then the order topology on A agrees with its subspace topology TA? Justify your answer.
Transcribed Image Text:(ii) Endow R with its order topology. Is it true that if A C R has no minimum and maximum, then the order topology on A agrees with its subspace topology TA? Justify your answer.
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