# Functional Analysis MCQs Quiz.4

Functional Analysis is most important for university entrance tests as well as jobs. If you’re finding functional analysis MCQs then you’re in the right place where you will get important past papers quizzes. Most of the MCQ quizzes in Dream Mathematic include past paper solutions. With their many multiple choice questions quizzes, all these MCQ quizzes are important for competitive exams.

This is Quiz.4 of functional analysis multiple choice questions, if you want to practice functional analysis multiple choice questions must solve other quizzes which are on functional analysis.

### Functional Analysis MCQs Quizzes:

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Functional Analysis MCQs Quiz.4

In the Functional Analysis MCQs Quiz, we are sharing Questions with you on Dual Spaces, Inner product space, Banach space, Subspaces, and Metric Spaces  MCQs questions to help us to increase our knowledge.

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1. Let N be a finite-dimensional normed space, then N is isomorphic to

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2. The dual space of c and c0

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3. A subspace Y of a complete metric space is complete if and only if Y is?

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4. [-1,1] is a neighborhood of?

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5. An open ball in R with the usual metric is?

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6. In the metric spaces (R, d) the closure of Q is?

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7. The dual space of Rn is:

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8. A subset " A " of " M " is said to be dense in " M " if the closure of " A " is?

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9. Let V be a normed space and U be a subspace of V. Let f0 be a bounded linear functional on V with norm || f0 ||. Then f0 has a continuous linear extension f defined on V such that || f || = || f0 || is a statement of

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10. Let V be an inner product space then V is also:

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11. Let V be a complete inner product space, the V is called:

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12. Let the dimension of a normed space N is n, then the dimension of its dual space N* is:

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13. The dual space of l1 is:

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14. Which of the following is a normed space which is not inner product space?

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15. Let N and M be Banach spaces and T : N → M be a bijective continuous linear operator.
Then T is a: