and Jasl Hce VAc X,A +02A6 coPpectVAC X,A 7 AB coMpictSubspuce in (iIR, ToslA GRBut A+B , A i5 closedCIR Jace Ifinile CRIAE Tror)compact ond net desed inEo A is=) Ciny nRnite setisCR Jell 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.

Prove that if A⊂X, A≠∅, then A is compact subspace of ℝ, τcof. Definition: (Cofinite topology) The…

Answered: and dast He VAc X,A +0 Ab compect…

and dast He VAc X,A +0 Ab compect Subspuce in (IR, Tod A GR A+B, As closed o A B fioe CRIAEJcor) CIR Je I finile c RIAE TroF) is cormpact ond set descel in CRi Jefl But in any ninite set

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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Concept explainers

Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.

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and Jasl Hce VAc X,A +02A6 coPpect
VAC X,A 7 AB coMpict
Subspuce in (iIR, Tosl
A GR
But A+B , A i5 closed
CIR Jace I
finile CRIAE Tror)
compact ond net desed in
Eo A is
=) Ciny nRnite set
is
CR Jell

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.

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