Definition: A space X is compact provided that every open cover of X has a finitesubcover. Equivalently, X is compact provided that for every collection O of opensets whose union equals X, there is a finite subcollection {O;}\1 of O whose unionequals X. A subspace A of a space X is compact provided that A is a compacttopological space in its subspace topology. e HWprove that the following interels(with usual gubspace top]are not compact.or [a,b J

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Answered: Prove that the following intervals…

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Prove that the following intervals (with usual subspace top] are not campact. (-00,G], [an ∞)

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.2: Linear Independence, Basis, And Dimension

Problem 4AEXP

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Definition: A space X is compact provided that every open cover of X has a finite
subcover. Equivalently, X is compact provided that for every collection O of open
sets whose union equals X, there is a finite subcollection {O;}\1 of O whose union
equals X. A subspace A of a space X is compact provided that A is a compact
topological space in its subspace topology.

e HW
prove that the following interels
(with usual gubspace top]
are not compact.
or [a,b J

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