Topological houses

Many properties of houses are of topological nature. The problem
of three-dimensional encoding is solved here by first giving an
axiomatic description of a simplified concept of "house" as a
certain generalisation of a cw-complex and, secondly, by
generalising local observation structures of embedded
unconnected planar graphs to the three-dimensional case and
proving that they allow retrieving all topological properties of
these simplified houses. In the more general case of an
architectural complex (a certain generalisation of a "house")
still much topolgical information is kept in these structures
still making them a useful approach to encoding topological
spaces. Finally, a lossless representation of observation
structures in a relational database scheme which we call PLAV
(Points, Lines, Areas, Volumes) is given. We expect PLAV to be
useful for encoding higher dimensional (architectural)
space-time complexes.

Schlagworte / Keywords: topologisches Modell; Gebäudeproduktmodell