Let X = {a, b, c, d,e} and let T= { X, Ø, {a}, {a,d}, {a,e} }, then * O (X,T) is Hausdorff and connected O (X, T) is not Hausdorff but it is connected O (X, T) is neither Hausdorff nor connected O (X,T) is not connected but it is Hausdorff

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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O fis a homeomorphism
O fis not continuous
Let X = {a, b, C, d,e} and let T = { X, Ø, {a}, {a,d}, {a,e}}, then *
O (X,T) is Hausdorff and connected
O (X, T) is not Hausdorff but it is connected
O (X, T) is neither Hausdorff nor connected
O (X,T) is not connected but it is Hausdorff
R is not connected if T is *
Transcribed Image Text:O fis a homeomorphism O fis not continuous Let X = {a, b, C, d,e} and let T = { X, Ø, {a}, {a,d}, {a,e}}, then * O (X,T) is Hausdorff and connected O (X, T) is not Hausdorff but it is connected O (X, T) is neither Hausdorff nor connected O (X,T) is not connected but it is Hausdorff R is not connected if T is *
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