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Assignment # 2
Topology (Mth634)
(Fall 2019)
Total marks: 10
DON’T MISS these important instructions:
Due date: 29/01/2020• Upload assignments properly through LMS, (No Assignment will be accepted through email).
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• Solve the assignment on MS word document and upload your word (.doc) files only. Don’t send image.Question 1: Marks 5
Let be a CoFinite Topology on a set X. Show that is separable.
Question 2: Marks 5
Consider X=R(Set of real numbers) with usual topology and consider the following collections of subsets of X .
U={(n,n) n ϵ N} V={[n,n+1] n ϵ Z}Determine whether these collections form open covers for the usual topology on R. Justify your answer.

Assignment No.1 MTH634 (Fall 2019)
Maximum Marks: 15
Due Date:1st December ,2019DON’T MISS THESE: Important instructions before attempting the solution of this assignment:
• To solve this assignment, you should have good command over 115 lectures.
Try to get the concepts, consolidate your concepts and ideas from these questions which you learn in the these lectures.
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Try to make solution by yourself and protect your work from other students, otherwise you and the student who send same solution file as you will be given zero marks.
Also remember that you are supposed to submit your assignment in Word format any other like scan images etc will not be accepted and we will give zero marks correspond to these assignments.Question 1: Marks:10
Let be the topology on N which consists of and all subsets of N of the form where n∈N. Determine the closed subsets of (N,τ).
Question 2: Marks: 5
Consider the topology
on . Determine the derived sets of .