From: Michael Barr <barr@math.mcgill.ca>
To: Urs Schreiber <urs.schreiber@googlemail.com>, categories@mta.ca
Subject: Re: 'Directed Algebraic Topology'
Date: Mon, 21 Sep 2009 11:56:47 -0400 (EDT) [thread overview]
Message-ID: <E1Mply1-0004D6-7j@mailserv.mta.ca> (raw)
One obvious thing that comes to mind are asymmetric spaces--a metric
without the symmetry axiom. This can obviously be extended to uniform
spaces, although I am not aware anyone has. As for topological spaces, I
know of nothing there.
Michael
On Mon, 21 Sep 2009, Urs Schreiber wrote:
> Marco Grandis wrote:
>
>> My book
>>
>> 'Directed Algebraic Topology'
>> Models of non-reversible worlds
>>
>> has appeared, at Cambridge University Press.
>
> In that context I am wondering about the following:
>
> it would be nice to have a notion of directed topological space that
> would extend the relation between (nice) topological spaces and
> oo-groupoids to one between (nice) directed topological spaces and
> (oo,1)-categories.
>
> More generally, it would be nice to have a notion of "r-directed
> topological space" for r in N that would extend the relation between
> (nice) topological spaces and oo-groupoids to one of (nice)
> "r-directed spaces" and (oo,r)-cateories.
>
> (Probably such a notion of directed spaces can't be supporrted by
> plain topological spaces with direction information, but requires
> filtered directed spaces or the like. )
>
> Has anything like this been considered?
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next reply other threads:[~2009-09-21 15:56 UTC|newest]
Thread overview: 11+ messages / expand[flat|nested] mbox.gz Atom feed top
2009-09-21 15:56 Michael Barr [this message]
-- strict thread matches above, loose matches on Subject: below --
2009-09-29 11:42 Marco Grandis
2009-09-28 18:43 George Janelidze
2009-09-22 21:01 Martin Escardo
2009-09-22 13:12 Gaucher Philippe
2009-09-22 13:05 Peter Bubenik
2009-09-22 9:00 Urs Schreiber
2009-09-22 8:37 Marco Grandis
2009-09-21 23:15 George Janelidze
2009-09-21 9:44 Urs Schreiber
2009-09-18 15:23 Marco Grandis
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