6) (ii) Consider the collection of subsets of R given by B= {[a,b]|a E R, b E R and b > a}. Can this be a basis for a topology on R? If so, prove it. If not, show why not. [Be sure that you noticed the condition b 2 a.] (ii) Consider the collection of subsets of R given by B= {[a,b]|a € R, b E R and b > a}. Can this be a basis for a topology on R? If so, prove it. If not, show why not. [Be sure that you noticed the condition b > a.]
6) (ii) Consider the collection of subsets of R given by B= {[a,b]|a E R, b E R and b > a}. Can this be a basis for a topology on R? If so, prove it. If not, show why not. [Be sure that you noticed the condition b 2 a.] (ii) Consider the collection of subsets of R given by B= {[a,b]|a € R, b E R and b > a}. Can this be a basis for a topology on R? If so, prove it. If not, show why not. [Be sure that you noticed the condition b > a.]
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
consider the collection of subsets
![(a, b) = {x E R|a < x < b}; [a, b) = {x E R|a <x <b}; (a, b] = {x ER
la < x < b} and [a, b] = {x € R[a <x< b}](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4035242d-f18b-4709-bb6e-951753bf8b42%2F8c21e6b1-e81e-4db5-bf34-156db8fb787e%2Fs5lgt8g_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(a, b) = {x E R|a < x < b}; [a, b) = {x E R|a <x <b}; (a, b] = {x ER
la < x < b} and [a, b] = {x € R[a <x< b}
![6) (ii) Consider the collection of subsets of R given by
B= {[a,b]|a E R, b E R and b > a}. Can this be a basis for a
topology on R? If so, prove it. If not, show why not. [Be sure that
you noticed the condition b > a.]
(ii) Consider the collection of subsets of R given by
B= {[a,b]|a E R, b E R and b > a}. Can this be a basis for a
topology on R? If so, prove it. If not, show why not. [Be sure that
you noticed the condition b > a.]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4035242d-f18b-4709-bb6e-951753bf8b42%2F8c21e6b1-e81e-4db5-bf34-156db8fb787e%2Fpkroed_processed.jpeg&w=3840&q=75)
Transcribed Image Text:6) (ii) Consider the collection of subsets of R given by
B= {[a,b]|a E R, b E R and b > a}. Can this be a basis for a
topology on R? If so, prove it. If not, show why not. [Be sure that
you noticed the condition b > a.]
(ii) Consider the collection of subsets of R given by
B= {[a,b]|a E R, b E R and b > a}. Can this be a basis for a
topology on R? If so, prove it. If not, show why not. [Be sure that
you noticed the condition b > a.]
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