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From: kj on 5 Apr 2010 08:03


This is the most basic question possible: a definition (I can't
find it online).

In a different thread (
<120e389f-6f19-49d9-b1f9-1240cff7eb8b(a)35g2000yqm.googlegroups.com>)
drhab <habrozius(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?

Thanks!

~K
From: cwldoc on 8 Apr 2010 21:18
>
>
> This is the most basic question possible: a
> definition (I can't
> find it online).
>
> In a different thread (
> <120e389f-6f19-49d9-b1f9-1240cff7eb8b(a)35g2000yqm.googl
> egroups.com>)
> drhab <habrozius(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?
>
> Thanks!
>
> ~K

I would think that for "quotient space X/A" to make sense, X would have to have some other structure, for example that of a group or ring.

(Then one would endow X/A with the quotient topology: a subset, U, of X/A is declared to be open iff p^(-1)(U) is open in X, where p:X->Q/A is the function that takes element x to the coset that contains it.)
From: Anand Joshi on 9 Apr 2010 03:38
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?
>
> Thanks!
>
> ~K

A quotient topology X/A defined when an equivalence relation is
defined on the topological space X such that A is a set of
representatives of equivalence classes. The map q is then the natural
projection onto the set of equivalence classes.
From: Link on 9 Apr 2010 03:53
On Apr 9, 12:38 am, Anand Joshi <ajoshi.u...(a)gmail.com> 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?
>
> > Thanks!
>
> > ~K
>
> A quotient topology X/A defined when an equivalence relation is
> defined on the topological space X such that A is a set of
> representatives of equivalence classes. The map q is then the natural
> projection onto the set of equivalence classes.

I think it might be 'Q' the Motorola phone, came out few years ago,
not sure who has rights or if it may be used for mathematics.

You may want to contact Jonathan Meyer.

mmm
From: Arturo Magidin on 9 Apr 2010 19:08
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
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