Topology Problems

Question

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 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.