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Jordan Surfaces in Discrete Antimatroid Topologies

  • Ralph Kopperman
  • John L. Pfaltz
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3322)

Abstract

In this paper we develop a discrete, T 0 topology in which (1) closed sets play a more prominent role than open sets, (2) atoms comprising the space have discrete dimension, which (3) is used to define boundary elements, and (4) configurations within the topology can have connectivity (or separation) of different degrees.

To justify this discrete, closure based topological approach we use it to establish an n-dimensional Jordan surface theorem of some interest. As surfaces in digital imagery are increasingly rendered by triangulated decompositions, this kind of discrete topology can replace the highly regular pixel approach as an abstract model of n-dimensional computational geometry.

Keywords

Closure Operator Discrete Topology Geometric Space Geometric Topology Digital Imagery 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Ralph Kopperman
    • 1
  • John L. Pfaltz
    • 2
  1. 1.City University of New YorkNew York
  2. 2.University of VirginiaCharlottesville

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