CSIR NET Follow
September 17, 2020 9:27 pm 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
see attached proof , 1/n is cauchy sequence but not convergent in N , So it is incomplete metric space
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
• Deepak singh
in metric space , cauchy sequence need not be convergent ..
• 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
• Sonika Jain
so how in ur example 1/n is cauchy but not convegent
• Sonika Jain
cauchy is always convergent and convergent is always cauchy
Deepak singh
this result is true only in real analysis not in metric space...
• Sonika Jain
so how its applied here
• Sonika Jain
in question it is metric and 1/n is sequence
see attached .. option b and d are correct.. 