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One of the fundamental questions in topology is the “extension problem.” This asks for criteria for being able to extend a map g: A → Y defined on a subspace A of X to all of X. Of course, this cannot always be done as is shown by the case A = Y = S n , X = D n+1.
KeywordsExact Sequence Base Point Commutative Diagram Homotopy Group Homotopy Theory
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