QuestionQuestion

1/
Let A=[a1,a2] and B=[b1,b2] and be closed and bounded intervals in R. In each of the following groups determine which of the four possible intersection values can be realized and which cannot for A and B in R. Depict those that can be realized and prove that the reminder cannot.
A – (0,0,0,0),(1,0,0,0),(0,1,0,0),(1,1,0,0)
B – (0,0,1,0),(1,0,1,0),(0,1,1,0),(1,1,1,0)

2/
Let A and B be closed sets in topological space X.
a/ prove that if I_(A,B)=(0,0,0,0) then A∩B=∅
b/ prove that if I_(A,B)=(1,0,0,0) then A∩B=∂A ∩ ∂B

3/
a/ provide an example demonstrating that ∂A need not equal ∂(int(A)).
b/ show that ∂A= ∂(int(A))for regularly closed sets A

Solution PreviewSolution 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.

    $20.00 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.

    Decision:
    Upload a file
    Continue without uploading

    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