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Boundary Presentation Using Abstract Cell Complexes

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Image Processing with Cellular Topology

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Abstract

This chapter describes the properties of abstract cell complexes. The definition of the dimension of cells is explained. It has been shown how the connectivity paradox can be solved by means of complexes. The notion of the smallest open neighborhoods and that of closures are introduced. It is shown how coordinates of cells can be defined, and the difference between the standard and combinatorial coordinates is being explained.

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References

  1. Listing J. Der Census räumlicher Complexe. Abhandlungen der Königlichen Gesellschaft der Wissenschaften zu Göttingen. 1862;10:97–182.

    Google Scholar 

  2. Hazewinkel M, editor. Hausdorff space. In: Encyclopedia of mathematics. Springer/Kluwer Academic Publishers; 1994/2001. ISBN 978-1-55608-010-4.

    Google Scholar 

  3. Whitehead JHC. Combinatorial homotopy. I. Bull Am Math Soc. 1949;55(5):213–45.

    Article  MathSciNet  Google Scholar 

  4. Warner S. Modern algebra. Dover Publications; 1990. p. 6.

    Google Scholar 

  5. Alexandroff P. Discrete spaces. Mat Sbornik. 1937;2:501–18.

    Google Scholar 

  6. Alexandroff P, Hopf H. Chapter 3: Topologie der Komplexe. In: Topologie II. Chelsea; 1935.

    MATH  Google Scholar 

  7. Aleksandrov PS. Chapter XVIII: topology. In: Aleksandrov AD, Kolmogorov AN, Lavrent’ev MA, editors. Mathematics/its content, methods and meaning. 2nd ed. MIT Press; 1956/1969.

    Google Scholar 

  8. Feng HY, Pavlidis T. IEEE Trans Circ Syst. 1975;22:427–39.

    Article  Google Scholar 

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Authors and Affiliations

  1. Computer Science Department, University of Applied Sciences Berlin, Berlin, Germany

    Vladimir Kovalevsky

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  1. Vladimir Kovalevsky
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Kovalevsky, V. (2021). Boundary Presentation Using Abstract Cell Complexes. In: Image Processing with Cellular Topology. Springer, Singapore. https://doi.org/10.1007/978-981-16-5772-6_2

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  • DOI: https://doi.org/10.1007/978-981-16-5772-6_2

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-16-5771-9

  • Online ISBN: 978-981-16-5772-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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