
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).
• All students are directed to use the font and style of text as is used in this document.
• This is an individual assignment, not group assignment, so keep in mind that you are supposed to submit your own, self made & different assignment even if you discuss the questions with your class fellows. All similar assignments (even with some meaningless modifications) will be awarded zero marks and no excuse will be accepted. This is your responsibility to keep your assignment safe from others.
• Above all instructions are for all assignments so may not be mentioned in future.
• Solve the assignment on MS word document and upload your word (.doc) files only. Don’t send image.Question 1: Marks 5
Let19cd580244cd4860ae26cf919da91c38image.png be a CoFinite Topology on a set X. Show that 866db31819064c3aa6e6dbb6fcbb77e4image.png 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:
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Try to get the concepts, consolidate your concepts and ideas from these questions which you learn in the these lectures.
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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 a55ec4d76146447eb239ea1d0be581bcimage.png where n∈N. Determine the closed subsets of (N,τ).
Question 2: Marks: 5
Consider the topology
9290773861d745eb89229487bce813a8image.png
on b3e1551ebd8348b0acca217be77227c6image.png . Determine the derived sets of .
MTH634 Assignment 2 Solutin and Discussion

Assignment # 2
Topology (Mth634)
(Fall 2019)
Total marks: 10
Due date: 29/01/2020DON’T MISS these important instructions:
• Upload assignments properly through LMS, (No Assignment will be accepted through email).
• All students are directed to use the font and style of text as is used in this document.
• This is an individual assignment, not group assignment, so keep in mind that you are supposed to submit your own, self made & different assignment even if you discuss the questions with your class fellows. All similar assignments (even with some meaningless modifications) will be awarded zero marks and no excuse will be accepted. This is your responsibility to keep your assignment safe from others.
• Above all instructions are for all assignments so may not be mentioned in future.
• 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.

please share idea?