Structure from appearance: topology with shapes, without points

@article{Haridis2020StructureFA,
  title={Structure from appearance: topology with shapes, without points},
  author={Alexandros Haridis},
  journal={Journal of Mathematics and the Arts},
  year={2020},
  volume={14},
  pages={199 - 238}
}
ABSTRACT A new methodological approach for the study of topology for shapes made of arrangements of lines, planes or solids is presented. Topologies for shapes are traditionally built on the classical theory of point-sets. In this paper, topologies are built with shapes, which are formalized as unanalyzed objects without points, and with structures defined from their parts. An interpretative, aesthetic dimension is introduced according to which the topological structure of a shape is not… 
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