Vinayaka Missions University 2008 M.Sc Mathematics SET TOPOLOGY AND THEORY OF RELATIVITY : t : Correspondence - Question Paper

COURSE CODE – 2030508
PG DEGREE exam - SEP 2008
M.SC (MATHS)
SET TOPOLOGY AND THEORY OF RELATIVITY
(For Candidate Admitted From Calendar Year 2007 On wards)
Time: three hours Max. Marks: 75
part – A
ans all the questions: 15 x one = 15
1. What is standard Topology?
2. If A is subspace of X and B is subs pall of Y what happen the
product?
3. What is haus doff space?
4. Whether the subspace of a haus doffs space is haus doffed or
not?
5. Comparing Box and product topology?
6. describe bounded diameter?
7. What is the image of compact space under a continuous map?
8. What is compact?
9. What is connected?
10. How can the Cartesian product of the indexed family is
denoted?
11. Write the 1st countable axiom?
12. What is dense?
13. Difference ranging from regular and normal?
14. A product of completely regular space is?
15. When the path component works?
part – B
ans any 5 questions: five x six = 30
16. a. describe i. Topological space, ii. Sub basis iii. Order
topology, iv. Product topology.
(Or)
b. describe i. Limit points ii. Projection prove that it Y is a
subspace of X and A = Xny then A is closed in Y?
17. a. Show that every finite point in a set in a haus doff space is
closed?
(Or)
b. Show that U is open in X and A is closed in X then U-A is
closed in X and A-U is closed in X?
18. a. describe ball, metrizable and provide an example?
(Or)
b. describe i. Box Topology ii. Cartesian product.
iii. Metric Topology?
19. a. State and prove intermediate value theorem?
(Or)
b. State and prove Extreme Value theorem?
20. a. describe i. Separation ii. Regular, iii. Normal and provide an
example.
(Or)
b. Proves subspace of regular space is regular.
part -C
ans any 2 questions: two x 15 = 30
21. State and prove i. Pasting lemma, ii. Maps into products?
22. Prove a finite cartesion product of connected space is
connected?
23. Prove tube lemma?
24. State and prove urysolm lemma?
25. State and prove tietze Extension theorem?

Earning:   Approval pending.