MTH634 - Topology

Assignment # 2 Topology (Mth634) (Fall 2019) Total marks: 10 Due date: 29/01/2020 DON’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[image: 5PIA7AR.png] be a Co-Finite Topology on a set X. Show that [image: OYmrBDi.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 ,2019 DON’T MISS THESE: Important instructions before attempting the solution of this assignment: • To solve this assignment, you should have good command over 1-15 lectures. Try to get the concepts, consolidate your concepts and ideas from these questions which you learn in the these lectures. • Upload assignments properly through LMS, No Assignment will be accepted through email. • Write your ID on the top of your solution file. Don’t use colorful back grounds in your solution files. Use Math Type or Equation Editor etc for mathematical symbols. You should remember that if we found the solution files of some students are same then we will reward zero marks to all those students. 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 [image: 4eRfl0J.png] where n∈N. Determine the closed subsets of (N,τ). Question 2: Marks: 5 Consider the topology [image: hH3HfZ6.png] on [image: Bn2NOwz.png] . Determine the derived sets of .