Topological Digital Topology

  • Ralph Kopperman
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2886)


The usefulness of topology in science and mathematics means that topological spaces must be studied, and computers should be used in this study. We discuss how many useful spaces (including all compact Hausdorff spaces) can be approximated by finite spaces, and these finite spaces are completely determined by their specialization orders. As a special case, digital n-space, used to interpret Euclidean n-space and in particular, the computer screen, is also dealt with in terms of the specialization. Indeed, algorithms written using the specialization are comparable in difficulty, storage usage and speed to those which use the traditional (8,4), (4,8) and (6,6) adjacencies, and are of course completely representative of the spaces.


Digital topology general topology T0-space specialization (order) connected ordered topological space (COTS) Alexandroff space Khalimsky line digital n-space metric and polyhedral analogs chaining maps calming maps normalizing maps inverse limit Hausdorff reflection skew (=stable) compactness (graph) path and arc connectedness and components (topological) adjacency Jordan curve robust scene cartoon 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Ralph Kopperman
    • 1
  1. 1.Department of MathematicsCity College of New YorkNew YorkUSA

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