QuestionQuestion

Q1/Determine ∂A in each case
A=(0,1]in the lower limit topology on R
A={a} in X={a,b,c} with topology {X,∅,{a},{a,b}}
.A={a,c} in X={a,b,c} with topology {X,∅,{a},{a,b}}
A={b} in X={a,b,c} with topology {X,∅,{a},{a,b}}
A=(-1,1)∪{2} in the standard topology on R
A=(-1,1)∪{2} in the lower limit topology on R
A={(x,0)ϵR^2 |xϵR}with the standard topology
A={(x,0)ϵR^2 |xϵR} with the vertical interval topology

Q2/for nϵZ determine ∂({n}) in the digital line topology considering separately the cases where n is even and n is odd. Discuss how your results for ∂({n}) reflect the digital image display structure modeled by the digital line?

Q3/Determine the boundary of each the following subsets of R² in the standard topology
A={(x,x)ϵR^2 |ϵR}
A={(x,y)ϵR^2 |x>0,y≠0}
A={(1/n,0)ϵR^2 |n ϵz_+ }
A={(x,y)ϵR^2 |0≤x^2-y^2<1}

Q4/Determine ∂([0,1]) in R with the finite complement topology. Justify your result.?

Q5/
a) Give an example to show that the implication A=C-B→A∪B=C fails in general.
b) Show that if B⊆C then the implication in (a) holds.

Q6/
a) Show that in general the implication A∪B=C→A=c-B fails.
b) Under what condition on A and B in implication in ( a ) is true?

Q7/ Show that ∂A ∪ in A=cl A implies in A=clA-∂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.

Topology Problems
    $30.00 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