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Functional Analysis
Q. If A is a subspace of l^∞ consisting of all sequence of 0 and 1. What is the induced metric on A?
Functional Analysis
Q.Show that d(x,y)=Sup|∑_j-n_j |, j∈N satisfy triangular property.
Functional Analysis
Q.Let D be a metric on X determined all constant k s.t
(i) kd is a metric
(ii)(k+d) is a metric
(Prove it)
(i) kd is a metric
(ii)(k+d) is a metric
(Prove it)
Functional Analysis
Q.Find all metric on a set X consisting of one point and consisting of two points.
Functional Analysis
Is the real line a metric space?
Functional Analysis
Q. Which of the following sets are countable or uncountable.
(i) set of real numbers
(ii) set of complex numbers
(i) set of real numbers
(ii) set of complex numbers
Functional Analysis
Q. Which of the following sets are countable or uncountable.
(i)set of negative integers
(ii) set of rational numbers
(i)set of negative integers
(ii) set of rational numbers
Functional Analysis
Q. Which of the following sets are countable or uncountable.
(i) set of natural numbers
(ii) set of whole numbers
(iii) set of positive integers
(i) set of natural numbers
(ii) set of whole numbers
(iii) set of positive integers
Functional Analysis
show that the absolute value of a linear functional has the subadditive and positive homogeneous properties.
Functional Analysis
show that a norm on a vector space X is a sublinear functional on X
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#340153 on Dec 2023
#340153 on Dec 2023