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From: Anand Joshi on 11 Apr 2010 03:19
On Apr 9, 4:08 pm, Arturo Magidin <magi...(a)member.ams.org> wrote:
> On Apr 5, 5:03 am, kj <no.em...(a)please.post> wrote:
>
> > This is the most basic question possible: a definition (I can't
> > find it online).
>
> > In a different thread (
> > <120e389f-6f19-49d9-b1f9-1240cff7e...(a)35g2000yqm.googlegroups.com>)
>
> > drhab <habroz...(a)gmail.com> writes:
> > >...let A be a subset of topological space X. Let q:X->X/A be the
> > >quotient map...
>
> > How is the quotient space X/A defined in this case?
>
> To me, the reasonable interpretation is that we "collapse" A into a
> single point. That is, we define an equivalence relation ~ on X by
> "x~y if and only if x=y, or both x and y are in A" and then consider
> the quotient X/~. This will yield a quotient in which all of A maps to
> a single point, and the points outside of A are not collapsed
> together.
>
> --
> Arturo Magidin

I agree with this. In algebraic topology, it typically means joining
the points in A together. e.g. [x,y]/{x,y} is S1.
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