University Of Hyderabad,Entrance Examination-2016-M,Sc Master In Public Health Question Paper

 University Name : University Of Hyderabad    

Department :  Entrence Examination  

Exam Year : 2016

Subject: Master In Public Health

Code No : K-15

Booklet Code No: 

Time : 2.00 Hours

Maximum Marks : 100

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University Of Hyderabad,Entrance Examination-2021-M,Ed Master of Education Question Paper

 University Name : University Of Hyderabad    

Department :  Entrence Examination  

Exam Year : 2021

Subject: M,Ed Master of Education

Code No : Z-31

Booklet Code No: 

Time : 2.00 Hours

Maximum Marks : 100

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University Of Hyderabad,Entrance Examination-2020-M,Ed Master of Education Question Paper

 University Name : University Of Hyderabad    

Department :  Entrence Examination  

Exam Year : 2020

Subject: M,Ed Master of Education

Code No : W-31

Booklet Code No: 

Time : 2.00 Hours

Maximum Marks : 100

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220 SET TOPOLOGY AND FUNCTIONAL ANALYSIS Punjabi University 2008 Question Paper

220 SET TOPOLOGY AND FUNCTIONAL ANALYSIS Punjabi University 2008 Question Paper
Punjabi University Question Paper
M.Sc Mathematics DEGREE EXAMINATION, 2008
MATHEMATICS
Second Year
Paper - VI
220 SET TOPOLOGY AND FUNCTIONAL ANALYSIS
(Revised Regulations)
(Including Lateral Entry)
2nd June) (Time: 3 Hours
Maximum: 100 Marks

PART-A (8×5=40)
Answer any EIGHT questions
All questions carry equal marks

1. Define the open set in a metric space. If X is a metric space, prove that any union of open sets in X is open.

2. Define the terms:
a) Discrete Topology
b) Complete Metric space
c) Sub-base


3. Prove that any continuous image of a compact space is compact..

4. State Urysohn’s lemma.

5. Define the terms:
a) Connected space
b) Connected subspace
c) Disconnected space

6. Prove that the components of a totally disconnected space are its points.

7. State and prove the Schwarz inequality.

8. State the open mapping theorem.

9. Give an example of a Hilbert space.

10. Let N and N' be normed linear spaces and T a linear transformation of N into N'. Then prove the following conditions on T are all equivalent to one another.

PART-B (3×20=60)
Answer any THREE questions
All questions carry equal marks

11. a) State and prove Cantor’s intersection theorem.

b) Let X be a topological space and A an arbitrary subset of X. Prove that ={x : each neighbourhood of x intersects A}.

12. a) State and prove Tychonoff’s theorem.

b) Let X and Y be metric spaces and f a mapping of X into Y. Then prove that f is continuous if and only if, f -1 (G) is open in X whenever G is open in Y.

13. Prove that a subspace of the real line R is connected if any only if, it is an interval. In particular, show that R is connected.

14. State and prove Hahn-Banach theorem.

15. Prove that every non-zero Hilbert space contains a complete orthonormal set.

220 SET TOPOLOGY AND FUNCTIONAL ANALYSIS Punjabi University 2008 Question Paper

220 SET TOPOLOGY AND FUNCTIONAL ANALYSIS Punjabi University 2008 Question Paper
Punjabi University Question Paper
M.Sc Mathematics DEGREE EXAMINATION, 2008
MATHEMATICS
Second Year
Paper - VI
220 SET TOPOLOGY AND FUNCTIONAL ANALYSIS
(Revised Regulations)
(Including Lateral Entry)
2nd June) (Time: 3 Hours
Maximum: 100 Marks

PART-A (8×5=40)
Answer any EIGHT questions
All questions carry equal marks

1. Define the open set in a metric space. If X is a metric space, prove that any union of open sets in X is open.

2. Define the terms:
a) Discrete Topology
b) Complete Metric space
c) Sub-base


3. Prove that any continuous image of a compact space is compact..

4. State Urysohn’s lemma.

5. Define the terms:
a) Connected space
b) Connected subspace
c) Disconnected space

6. Prove that the components of a totally disconnected space are its points.

7. State and prove the Schwarz inequality.

8. State the open mapping theorem.

9. Give an example of a Hilbert space.

10. Let N and N' be normed linear spaces and T a linear transformation of N into N'. Then prove the following conditions on T are all equivalent to one another.

PART-B (3×20=60)
Answer any THREE questions
All questions carry equal marks

11. a) State and prove Cantor’s intersection theorem.

b) Let X be a topological space and A an arbitrary subset of X. Prove that ={x : each neighbourhood of x intersects A}.

12. a) State and prove Tychonoff’s theorem.

b) Let X and Y be metric spaces and f a mapping of X into Y. Then prove that f is continuous if and only if, f -1 (G) is open in X whenever G is open in Y.

13. Prove that a subspace of the real line R is connected if any only if, it is an interval. In particular, show that R is connected.

14. State and prove Hahn-Banach theorem.

15. Prove that every non-zero Hilbert space contains a complete orthonormal set.