[ALGTOP-L] What kinds of topologies do these so-called "co-exact properties" describe?

Tim Porter t.porter at bangor.ac.uk
Sun Nov 2 07:54:08 EST 2008

Dear All,
A quite useful way into this subject is via the Qualitative Spatial  
Reasoning group at the University of leeds.


Their work looks at many of the aspects of the theory of region based  
calculi, applications of mixed modal logical models, etc. but also  
practical applications of all this to Geographical Information Systems.

The ideas are not always easy, but actually provide a wide range of  
approachable topics for student  project work in topology or logic.

This is not of course the only research group working in that area,  
there are many such, and unfortunately that site does not have many  
external links to other work.

Hope this helps.

Tim Porter

Quoting Albretch Mueller <lbrtchx at gmail.com>:

>  Hi,
> ~
>  to me properties such as defining "regions" and the containment
> relations between any of these two "regions" (in-, outside proper or
> bordering from the in-, outside) are topological in nature, but I am
> not well-versed in topology so I come to ask here
> ~
> // __ http://socrates.berkeley.edu/~fitelson/few/few_07/mumma.pdf
> ~
>  "To explain the division of labor between text and diagram, Manders
> distinguishes between the exact and co-exact properties of diagrams.
> Any one of Euclid?s diagrams contains a collection of spatially
> related magnitudes?e.g. lengths, angles, areas. For any two magnitudes
> of the same type, one will be greater than another, or they will be
> equal. These relations comprise the exact properties of the diagram.
> How these magnitudes relate topologically to one another? i.e. the
> regions they define, the containment relations between these
> regions?comprise the diagram?s co-exact properties. Diagrams of a
> single triangle, for instance, vary with respect to their exact
> properties.
>  That is, the lengths of the sides, the size of the angles, the area
> enclosed, vary. Yet with respect to their co-exact properties the
> diagrams are all the same. Each consists of three bounded linear
> regions, which together define an area."
> ~
>  Any literature that would help me ground myself on these topics?
> ~
>  Thanks
>  lbrtchx
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