PSSOU MA/MSC (Mathematics) Previous Topology (L–291) Solved Assignment 2025

(Assignment—1) 
Section—A 
1. The set of negative integers having the least upper bound is .................... . 
2. The complement of open set is ..................... . 
3. If A and B are subsets of a metric space, then (A B)
  
 4. In a metric space every derived set is ................... . 
5. Every metric space is not a ....................... . 
6. A compact subset of a Housdorff spaces is .................. . 
7. A product of regular space is .................. . 
8. A subspace of normal space is .................... . 
.................. . 
Section—B 
9. Define linear orders. 
10. Define bounded and unbounded metric space. 
11. Define relative topology. 
12. Define homeomorphism of topological space. 
13. Define path connected space. 
14. Define normal space. 
Section—C 
15. State and prove Zorn’s lemma. 
(Assignment—2) 
16. In a metric space, prove that every open sphere is an open set. 
17. If X is connected, then prove that (X)
 f
 is connected for any continuous map 
18. Prove that linearly ordered space are normal.