Alternate product adjacencies in digital topology

Laurence Boxer
DOI: https://doi.org/10.4995/agt.2018.7146

Abstract

We study properties of Cartesian products of digital images, using a variety of adjacencies that have appeared in the literature.

Keywords

digital topology; digital image; retraction; approximate fixed point property; continuous multivalued function; shy map

Subject classification

54C99; 05C99.

Full Text:

PDF

References

C. Berge, Graphs and hypergraphs, 2nd edition, North-Holland, Amsterdam, 1976.

K. Borsuk, Theory of retracts, Polish Scientific Publishers, Warsaw, 1967.

L. Boxer, Digitally continuous functions, Pattern Recognition Letters 15 (1994), 833-839. https://doi.org/10.1016/0167-8655(94)90012-4

L. Boxer, A classical construction for the digital fundamental group, Pattern Recognition Letters 10 (1999), 51-62.

L. Boxer, Properties of digital homotopy, Journal of Mathematical Imaging and Vision 22 (2005), 19-26. https://doi.org/10.1007/s10851-005-4780-y

L. Boxer, Digital products, wedges, and covering spaces, Journal of Mathematical Imaging and Vision 25 (2006), 159-171. https://doi.org/10.1007/s10851-006-9698-5

L. Boxer, Remarks on digitally continuous multivalued functions, Journal of Advances in Mathematics 9, no. 1 (2014), 1755-1762.

L. Boxer, Digital shy maps, Applied General Topology 18, no. 1 (2017), 143-152. https://doi.org/10.4995/agt.2017.6663

L. Boxer, Generalized normal product adjacency in digital topology, Applied General Topology 18, no. 2 (2017), 401-427. https://doi.org/10.4995/agt.2017.7798

L. Boxer, O. Ege, I. Karaca, J. Lopez, and J. Louwsma, Digital fixed points, approximate fixed points and niversal unctions, Applied General Topology 17, no. 2 (2016), 159-172. https://doi.org/10.4995/agt.2016.4704

L. Boxer and I. Karaca, Fundamental groups for digital products, Advances and Applications in Mathematical Sciences 11, no. 4 (2012), 161-180.

L. Boxer and P. C. Staecker, Connectivity preserving multivalued functions in digital topology, Journal of Mathematical Imaging and Vision 55, no. 3 (2016), 370-377. https://doi.org/10.1007/s10851-015-0625-5

L. Boxer and P.C. Staecker, Remarks on pointed digital homotopy, Topology Proceed-ings 51 (2018), 19–37.

L. Chen, Gradually varied surfaces and its optimal uniform approximation, SPIE Proceedings 2182 (1994), 300–307. https://doi.org/10.1117/12.171078

L. Chen, Discrete surfaces and manifolds, Scientific Practical Computing, Rockville, MD, 2004.

C. Escribano, A. Giraldo and M. Sastre, Digitally Continuous Multivalued Functions, in: Discrete Geometry for Computer Imagery, Lecture Notes in Computer Science, v. 4992, Springer, 2008, 81-92. https://doi.org/10.1007/978-3-540-79126-3_9

C. Escribano, A. Giraldo and M. Sastre, Digitally continuous multivalued functions, morphological operations and thinning algorithms, Journal of Mathematical Imaging and Vision 42 (2012), 76-91. https://doi.org/10.1007/s10851-011-0277-z

A. Giraldo and M. Sastre, On the composition of digitally continuous multivalued functions, Journal of Mathematical Imaging and Vision 53, no. 2 (2015), 196-209. https://doi.org/10.1007/s10851-015-0570-3

F. Harary, On the composition of two graphs, Duke Mathematical Journal 26, no. 1 (1959), 29-34. https://doi.org/10.1215/S0012-7094-59-02603-1

F. Harary and C. A. Trauth, Jr., Connectedness of products of two directed graphs, SIAM Journal on Applied Mathematics 14, no. 2 (1966), 250-254. https://doi.org/10.1137/0114024

S.-E. Han, Computer topology and its applications, Honam Math. Journal 25 (2003), 153-162.

S.-E. Han, Non-product property of the digital fundamental group, Information Sciences 171 (2005), 73-91. https://doi.org/10.1016/j.ins.2004.03.018

E. Khalimsky, Motion, deformation, and homotopy in finite spaces, in: Proceedings IEEE International Conference on Systems, Man, and Cybernetics, 1987, 227-234.

V. A. Kovalevsky, A new concept for digital geometry, Shape in Picture, Springer-Verlag, New York, 1994, pp. 37-51.

A. Rosenfeld, "Continuous" functions on digital images, Pattern Recognition Letters 4 (1987), 177-184. https://doi.org/10.1016/0167-8655(86)90017-6

G. Sabidussi, Graph multiplication, Mathematische Zeitschrift 72 (1960), 446-457. https://doi.org/10.1007/BF01162967

R. Tsaur and M. Smyth, "Continuous" multifunctions in discrete spaces with applications to fixed point theory, in: Bertrand, G., Imiya, A., Klette, R. (eds.), Digital and Image Geometry, Lecture Notes in Computer Science, vol. 2243, pp. 151–162. SpringerBerlin / Heidelberg (2001). https://doi.org/10.1007/3-540-45576-0_5

J. H. van Lint and R. M. Wilson, A Course in combinatorics, Cambridge UniversityPress, Cambridge, 1992.

Abstract Views

6076
Metrics Loading ...

Metrics powered by PLOS ALM


Bookmark and Share

 

Cited-By (articles included in Crossref)

This journal is a Crossref Cited-by Linking member. This list shows the references that citing the article automatically, if there are. For more information about the system please visit Crossref site

1. Fixed poin sets in digital topology, 1
Laurence Boxer, P. Christopher Staecker
Applied General Topology  vol: 21  issue: 1  first page: 87  year: 2020  
doi: 10.4995/agt.2020.12091



Esta revista se publica bajo una licencia de Creative Commons Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional.

Universitat Politècnica de València

e-ISSN: 1989-4147   https://doi.org/10.4995/agt