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3) (i) Let X be a set containing elements a and b. Define T= {X, Ø, U| a E U and b E U}. This is a slight generalization of the particular point topology. Prove that this is a topology on X. (ii) Let X be a set containing at least three elements including a and b. Define T= {X, Ø, U| a E U or b E U}. Is this a topology on X? If so, prove it. If not, explain why not? (iii) Let X= {a, b}. Define T= {X, Ø, U] a E U or b E U}. topology on X? If so, prove it. If not, explain why not? Is this a

3) (i) Let X be a set containing elements a and b. Define T= {X, Ø, U| a E U and b E U}. This is a slight generalization of the particular point topology. Prove that this is a topology on X. (ii) Let X be a set containing at least three elements including a and b. Define T= {X, Ø, U| a E U or b E U}. Is this a topology on X? If so, prove it. If not, explain why not? (iii) Let X= {a, b}. Define T= {X, Ø, U] a E U or b E U}. topology on X? If so, prove it. If not, explain why not? Is this a

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.2: Vector Spaces
Problem 38E: Determine whether the set R2 with the operations (x1,y1)+(x2,y2)=(x1x2,y1y2) and c(x1,y1)=(cx1,cy1)...
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3) (i) Let X be a set containing elements a and b. Define T= {X, Ø, U| a E U and b E U}. This is a slight generalization of the particular point topology. Prove that this is a topology on X. (ii) Let X be a set containing at least three elements including a and b. Define T= {X, Ø, U\ a E U or b E U}. Is this a topology on X? If so, prove it. If not, explain why not? (iii) Let X= {a, b}. Define T= {X, Ø, U| a ¤ U or b E U}. Is this a topology on X? If so, prove it. If not, explain why not?
Transcribed Image Text:3) (i) Let X be a set containing elements a and b. Define T= {X, Ø, U| a E U and b E U}. This is a slight generalization of the particular point topology. Prove that this is a topology on X. (ii) Let X be a set containing at least three elements including a and b. Define T= {X, Ø, U\ a E U or b E U}. Is this a topology on X? If so, prove it. If not, explain why not? (iii) Let X= {a, b}. Define T= {X, Ø, U| a ¤ U or b E U}. Is this a topology on X? If so, prove it. If not, explain why not?
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