13. Homotopy Invariance of Homology; Exact Sequences - Pierre Albin

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Lecture 13 of Algebraic Topology course by Pierre Albin.
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I'm a bit confused by the definition of a good pair. Is there a closed subspace A of X (topological space) that is not a deformation retract of a neighborhood in X? The definition suggests that the answer is yes but I don't see how this is possible.

kyung-sukim
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Where can I find the proof that the prism decomposition that was used is indeed both a cover, and one where the interiors don't overlap? I've searched the term "prism" in both Hatcher and J. P. May and I haven't found anything.

thephysicistcuber
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Homology is dual to co-homology.
Homotopic equivalence = duality!

hyperduality