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Unformatted text preview: x X and every closed set A X with x / A , there is a function f j F with f j ( x ) > 0 and f j ( a ) = 0 for all a A In the next two problems you will need to know that the Mobius band M is the quotient space obtained from [0 , 1] [1 , 1] by identifying (0 ,t ) with (1 ,t ). Let q : [0 , 1] [1 , 1] M be the quotient map. 4. (a) Dene what it means to say that the subspace A is a deformation retract of the space X . (b) Notice that the image q ([0 , 1] 0) is a circle C 1 in M . Show C 1 a deformation retract of M . 5. (a) Dene what it means to say that the subspace A is a retract of the space X . (b) Notice that the image q ([0 , 1] { 1 ,1 } ) is also a circle C 2 in M . Is C 2 a retract of M ? Prove your answer is correct....
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 Spring '11
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 Logic, Topology

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