 # Topology Problems

## Question

1. Show that B={[a,b)⊂R a<b is a basis for a topology on R.

2. Determine which of the the following collections of subsets of are bases:
a) C1={(n,n+2)⊂R ,n ∈Z
b) C2={[a,b]⊂R,a<b
c) C3={[a,b]⊂R,a≤b
d) C4{(-x,x)⊂R,x∈R
e) C5={(a,b)∪{b+1}⊂R,a<b

3. Determine which of the following are open sets in R_(l ) in each case prove your assertation.
A=[4,5)
B={3}
C=[1,2]
D=(7,8)

4. In arithmetic progression in Z is a set A(a,b)={……,a-2b,a-b,a,a,a+b, a+2b,….} with a,b ∈ Z and b≠0 prove that the collection of arithmetic progression topology on Z.

5. Prove that, in a topological space X if U is open and C is closed then U-C is open and C – U is closed.

6. Which sets are closed sets in the finite complement topology on a topological space X?

7. Which sets are closed sets in excluded point topology EPXp on a set X?

8. Which sets are closed sets in particular point topology PPxp on a set X?

9. Show that a single-point set{n} is closed digital line topology if and only if n is even?

10. Prove that intervals of form [a,b) are closed in the lower limit topology on R?

11. Prove that on a finite set, the discrete topology is the only topology that is Housdorff?

12. Show that R in the finite complement topology is not Housdorff?

## Solution Preview

This material may consist of step-by-step explanations on how to solve a problem or examples of proper writing, including the use of citations, references, bibliographies, and formatting. This material is made available for the sole purpose of studying and learning - misuse is strictly forbidden. \$23.00 for this solution

PayPal, G Pay, ApplePay, Amazon Pay, and all major credit cards accepted.

### Find A Tutor

View available Topology Tutors

Get College Homework Help.

Are you sure you don't want to upload any files?

Fast tutor response requires as much info as possible.

SUBMIT YOUR HOMEWORK
We couldn't find that subject.
Please select the best match from the list below.

We'll send you an email right away. If it's not in your inbox, check your spam folder.

• 1
• 2
• 3
Live Chats