The path-connectedness in Z2 and Z3 and classical topologies

  • Walter Kropatsch
  • Pavel Pták
Structural Matching and Grammatical Inference
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1451)


The main problem we persue in this paper is the question of when a given path-connectedness in Z2 and Z3 coincides with a topological connectedness. We answer this question provided the path-connectedness is induced by a homogeneous and symmetric neighbourhood structure. On the way we make a study of topological structures, arguing that the point-neighbourhood formalism can be well applied in the digital picture investigations.


Topological Space Topological Structure Digital Picture Closure Operation Topological Category 
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 1998

Authors and Affiliations

  • Walter Kropatsch
    • 1
  • Pavel Pták
    • 2
  1. 1.Pattern Recognition and Image Proc. Group - PRIPVienna University of TechnologyViennaAustria
  2. 2.Faculty of Electrical EngineeringCenter for Machine Perception CMP - Czech Technical UniversityPraha 2Czech Republic

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