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

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.5: Applications Of Inner Product Spaces
Problem 61E
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PismS
O fis a homeomorphism but g is not
Let X = {a, b, c, d,e} and let T = { X, ø, {a}, {a,d}, {a,e}}, then*
%3D
(X, T) is not Hausdorff but it is connected
(X,T) is not connected but it is Hausdorff
(X, T) is neither Hausdorff nor connected
(X,T) is Hausdorff and connected
Let f be a mapping from ]o,2[ to [1,+*[ defined by f(x) = 1/x. Then *
f is a homeomorphism
None of the choices
f is not continuous
f is continuous but not a homeomorphism
Transcribed Image Text:PismS O fis a homeomorphism but g is not Let X = {a, b, c, d,e} and let T = { X, ø, {a}, {a,d}, {a,e}}, then* %3D (X, T) is not Hausdorff but it is connected (X,T) is not connected but it is Hausdorff (X, T) is neither Hausdorff nor connected (X,T) is Hausdorff and connected Let f be a mapping from ]o,2[ to [1,+*[ defined by f(x) = 1/x. Then * f is a homeomorphism None of the choices f is not continuous f is continuous but not a homeomorphism
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