Assignment # 2

Topology (Mth634)

(Fall 2019)

Total marks: 10
Due date: 29/01/2020

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Question 1: Marks 5

Let be a Co-Finite 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 ,2019

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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 .