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Singular homology algorithm for MA-spaces

ABSTRACT
The work on digitizing subspaces of the 2-dimensional Euclidean space with a certain digital approach is an important discipline in both digital geometry and topology. The present work considers Marcus-Wyse topological approach which was established for studying 2-dimensional digital spaces Z2. We introduce the digital singular homology groups of MA-spaces (M-topological space with an M-adjacency), and we compute singular homology groups of some certain MA-spaces, we give a formula for singular homology groups of 2-dimensional simple closed MA-curves, and an algorithm for determining homology groups of an arbitrary MA-space.
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PAPER SUBMITTED: 2019-09-06
PAPER REVISED: 2019-10-10
PAPER ACCEPTED: 2019-10-14
PUBLISHED ONLINE: 2019-11-02
DOI REFERENCE: https://doi.org/10.2298/TSCI190906403U
REFERENCES
  1. Arslan, H., et. al., Homology Groups of n-Dimensional Digital Images, Proceedings, 21th Turkish National Mathematics Symposium, Istanbul, Turkey, B (2008), pp. 1-13
  2. Han, S. E., Non-product Property of the Digital Fundamental Group, Information Sciences, 171 (2005), pp. 73-91
  3. Han, S. E., The k-Homotopic Thinning and a Torus-Like Digital Image in Zn, Journal of Mathematical Imaging and Vision, 31 (2008), pp. 1-16
  4. Han, S. E., Generalizations of Continuity of Maps and Homeomorphisms for Studying 2D Digital Topological Spaces and Their Applications, Topology and its Applications, 196 (2015), pp. 468-482
  5. Han, S. E., Yao, W., Homotopy Based on Marcus-Wyse, Topology and its Applications, 201 (2016), pp. 358-371
  6. Han, S. E., Almost Fixed Point Property for Digital Spaces Associated with Marcus-Wyse Topological Spaces, Journal of Nonlinear Science and Applications, 10 (2017), pp. 34-47
  7. Han, S. E., Yao, W., An MA-Digitization of Hausdorff Spaces By Using a Connectedness Graph of the Marcus-Wyse Topology, Discrete Applied Mathematics, 276 (2017), pp. 335-347
  8. Kong, T.Y., Rosenfeld, A., Topological Algorithms for Digital Image Processing, Elsevier Science, Amsterdam, Holland, 1996
  9. Rosenfeld, A., Digital Topology, American Mathematical Monthly, 86 (1979), pp. 76-87
  10. Rotman, J. J., An Introduction to Algebraic Topology, Springer-Verlag, New York, USA, 1998
  11. Slapal, J., Topological Structuring of the Digital Plane, Discrete Mathematics and Theoretical Computer Science, 15 (2013), pp. 165-176
  12. Vergili, T., Karaca, I., Some Properties of Homology Groups of Khalimsky Spaces, Mathematical Sciences Letters, 4 (2015), 2, pp. 131-140
  13. Wyse, F., Marcus, D., Solution to Problem 5712, American Mathematical Monthly, 77 (1970), 1119