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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 ad
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 1
wait , I am giving u proof
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Deepak singh 1
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
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 1 Best Answer
see attached .. option b and d are correct..
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sir please elaborate a little
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its result that in interval of type [a,b] , under usual metric is always complete metric space...
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here [0,1] what would be be usual topology or what would be metric defined
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usual metric , I.e |x-y|
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Deepak singh 1![best-answer]()
see attached proof , 1/n is cauchy sequence but not convergent in N , So it is incomplete metric space
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
so why we take some metric d ?
yes , you are correct , 0 is limit point and does not belongs to N
thats why its not convergent..
the metric that I have used in this is usual metric I.e |x-y|