O N 93%1 2:47A property is said to be a topologicalproperty if it is preserved byhomeomorphism. Suppose that R isequipped with the usual topology,then the boundedness and theclosedness are not topologicalproperties because *Ris homeomorphic to ]-co, 0][a,b] is not homeomorphic to la,b[Ris homeomorphic to ]-o, O[Ris homeomorphic to ]a,b[Which one of the followingstatements is true? *A subspace of an indiscrete spaceis not necessarily indiscreteA subspace of a discrete space isindiscreteEvery subspace of an indiscretespace is indiscreteA subspace of an indiscrete spaceis a discrete space 46 O 0 OON 93%2:47docs.google.com/forms(15We define the included pointtopology by Tp={ UCR;U=Ø or pEU}.Let A = [3,5[, then A is dense in R if *None of the choicesR is equipped with the usualtopologyRis equipped with Tp and p =3Ris equipped with Tp and p =5Let f be a mapping from [1,+0o[ to[1,+00[, defined by f(x)=x+1/x. Then *f is a homeomorphismf is not continuousNone of the choicesf is continuous but it is not ahomeomorphismA property is said to be a topologicalproperty if it is preserved by

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A property is said to be a topological property if it is preserved by homeomorphism. Suppose that R is equipped with the usual topology, then the boundedness and the closedness are not topological properties because * Ris homeomorphic to ]-oo, 0] O [a,b] is not homeomorphic to la,b[ O Ris homeomorphic to ]-co, 0[ Ris homeomorphic to ]a,b[

A property is said to be a topological property if it is preserved by homeomorphism. Suppose that R is equipped with the usual topology, then the boundedness and the closedness are not topological properties because * Ris homeomorphic to ]-oo, 0] O [a,b] is not homeomorphic to la,b[ O Ris homeomorphic to ]-co, 0[ Ris homeomorphic to ]a,b[

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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2B
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A property is said to be a topological property if it is preserved by homeomorphism. Suppose that R is equipped with the usual topology, then the boundedness and the closedness are not topological properties because O 1-00,0] is homeomorphic to [0,+[ O Ris homeomorphic to ]0, +[ R is homeomorphic to ]0,1[ [0,1] is not homeomorphic to ]0,1[
Just do B, C and D
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36. Prove that the relation of orthogonality in an inner product space is symmetric. 37. Prove that thn