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Sep 8, 2011 at 0:51 comment added Georges Elencwajg Dear Michael: yes, as shown by Torsten's and Ben's fine answers.
Sep 7, 2011 at 5:15 comment added Michael Thanks to Georges' for your answer. Would the answer be positive if we assume $X$, $Y$ and $Z$ are manifolds, which is really what I meant to ask but forgot to mention?
Sep 6, 2011 at 18:09 history edited Georges Elencwajg CC BY-SA 3.0
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Sep 6, 2011 at 16:57 comment added algori Georges -- that's a good example. However, I believe for reasonably nice spaces the statement should be true. I'm not sure what exactly the "reasonably nice" condition is, but I guess it would suffice to require that the 1-point compactifications of all spaces should be finite CW-complexes.
Sep 6, 2011 at 8:22 history edited Georges Elencwajg CC BY-SA 3.0
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Sep 6, 2011 at 7:30 history edited Georges Elencwajg CC BY-SA 3.0
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Sep 6, 2011 at 0:16 history answered Georges Elencwajg CC BY-SA 3.0