[ALGTOP-L] Question: non-locally contractible well-pointed space
Ricardo Andrade
randrade at math.stanford.edu
Mon Feb 13 20:39:24 EST 2012
Hi all,
I don't like spamming the list with questions. Nevertheless, I hope the
people here might be better equipped to answer my question.
I recently posted a question on mathoverflow
http://mathoverflow.net/questions/87387/well-pointed-space-which-is-not-locally-contractible
It asks specifically for an example of a well-pointed space in which no
(sufficiently small) neighbourhood of the base-point is contractible.
I did get a rather unexpected answer which is indeed very interesting, but
fails to do what I wanted. It seems to me that such a counter-example
would be a natural thing to look for. So I come to this list to see if
someone knows of another example of a well-pointed space for which there
is no basis of contractible neighbourhoods around the base-point.
[Real goal: I actually want the inclusion of the base-point to be tame in
the sense of Quinn's "Homotopically stratified sets". This means that in
the NDR-pair characterization of cofibrations, the homotopy H which
appears also verifies: H(x,t)=* (* is the base-point) implies x=* or t=1.]
Thanks in advance,
Ricardo
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