Sonika Jain Asked a Question
September 17, 2020 9:27 pmpts 30 pts
Example: Which of the following is/are true? (CSIR-NET June 2016) (,1) with the usual topology admits a metric which is complete. ,1) with the usual topology admits a metric which is not complete 3) L0,With the usual topology admits a metric which is not complete. with the usual topology admits a metric which is complete 4) tric
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  • Deepak singh thankyou
    see attached proof , 1/n is cauchy sequence but not convergent in N , So it is incomplete metric space
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    Sonika Jain
    ok but if we look at 1/ n then, for very large n belongs to natutal number N , 1/n becomes very small tha is it will go towards zero, isnt that true
  • Deepak singh
    wait , I am giving u proof
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  • Deepak singh
    in metric space , cauchy sequence need not be convergent ..
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  • Sonika Jain
    here answer given is 1 and 2 and 4 i jus cut it with pen reading ur answer but here example is also given
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  • Sonika Jain
    so how in ur example 1/n is cauchy but not convegent
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  • Sonika Jain
    cauchy is always convergent and convergent is always cauchy
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    Deepak singh
    this result is true only in real analysis not in metric space...
  • Sonika Jain
    so how its applied here
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  • Sonika Jain
    in question it is metric and 1/n is sequence
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  • Deepak singh Best Answer
    see attached .. option b and d are correct..
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    Sonika Jain
    sir please elaborate a little
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