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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
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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}
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.]
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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