- -

Fixed poin sets in digital topology, 1

RiuNet: Institutional repository of the Polithecnic University of Valencia

Share/Send to

Cited by

Statistics

Fixed poin sets in digital topology, 1

Show simple item record

Files in this item

dc.contributor.author Boxer, Laurence es_ES
dc.contributor.author Staecker, P. Christopher es_ES
dc.date.accessioned 2020-04-27T09:09:27Z
dc.date.available 2020-04-27T09:09:27Z
dc.date.issued 2020-04-03
dc.identifier.issn 1576-9402
dc.identifier.uri http://hdl.handle.net/10251/141555
dc.description.abstract [EN] In this paper, we examine some properties of the fixed point set of a digitally continuous function. The digital setting requires new methods that are not analogous to those of classical topological fixed point theory, and we obtain results that often differ greatly from standard results in classical topology. We introduce several measures related to fixed points for continuous self-maps on digital images, and study their properties. Perhaps the most important of these is the fixed point spectrum F(X) of a digital image: that is, the set of all numbers that can appear as the number of fixed points for some continuous self-map. We give a complete computation of F(Cn) where Cn is the digital cycle of n points. For other digital images, we show that, if X has at least 4 points, then F(X) always contains the numbers 0, 1, 2, 3, and the cardinality of X. We give several examples, including Cn, in which F(X) does not equal {0, 1, . . . , #X}. We examine how fixed point sets are affected by rigidity, retraction, deformation retraction, and the formation of wedges and Cartesian products. We also study how fixed point sets in digital images can be arranged; e.g., for some digital images the fixed point set is always connected. es_ES
dc.language Inglés es_ES
dc.publisher Universitat Politècnica de València es_ES
dc.relation.ispartof Applied General Topology es_ES
dc.rights Reconocimiento - No comercial - Sin obra derivada (by-nc-nd) es_ES
dc.subject Digital image es_ES
dc.subject Fixed point es_ES
dc.subject Retraction es_ES
dc.title Fixed poin sets in digital topology, 1 es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.4995/agt.2020.12091
dc.rights.accessRights Abierto es_ES
dc.description.bibliographicCitation Boxer, L.; Staecker, PC. (2020). Fixed poin sets in digital topology, 1. Applied General Topology. 21(1):87-110. https://doi.org/10.4995/agt.2020.12091 es_ES
dc.description.accrualMethod OJS es_ES
dc.relation.publisherversion https://doi.org/10.4995/agt.2020.12091 es_ES
dc.description.upvformatpinicio 87 es_ES
dc.description.upvformatpfin 110 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 21 es_ES
dc.description.issue 1 es_ES
dc.identifier.eissn 1989-4147
dc.relation.pasarela OJS\12091 es_ES
dc.relation.references C. Berge, Graphs and Hypergraphs, 2nd edition, North-Holland, Amsterdam, 1976. es_ES
dc.relation.references L. Boxer, Digitally continuous functions, Pattern Recognition Letters 15 (1994), 833-839. https://doi.org/10.1016/0167-8655(94)90012-4 es_ES
dc.relation.references L. Boxer, A classical construction for the digital fundamental group, Journal of Mathematical Imaging and Vision 10 (1999), 51-62. https://doi.org/10.1023/A:1008370600456 es_ES
dc.relation.references L. Boxer, Continuous maps on digital simple closed curves, Applied Mathematics 1 (2010), 377-386. https://doi.org/10.4236/am.2010.15050 es_ES
dc.relation.references 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 es_ES
dc.relation.references L. Boxer, Alternate product adjacencies in digital topology, Applied General Topology 19, no. 1 (2018), 21-53. https://doi.org/10.4995/agt.2018.7146 es_ES
dc.relation.references L. Boxer, Fixed points and freezing sets in digital topology, Proceedings, 2019 Interdisciplinary Colloquium in Topology and its Applications, in Vigo, Spain; 55-61. es_ES
dc.relation.references L. Boxer, O. Ege, I. Karaca, J. Lopez, and J. Louwsma, Digital fixed points, approximate fixed points, and universal functions, Applied General Topology 17, no. 2 (2016), 159-172. https://doi.org/10.4995/agt.2016.4704 es_ES
dc.relation.references L. Boxer and I. Karaca, Fundamental groups for digital products, Advances and Applications in Mathematical Sciences 11, no. 4 (2012), 161-180. es_ES
dc.relation.references L. Boxer and P. C. Staecker, Remarks on fixed point assertions in digital topology, Applied General Topology 20, no. 1 (2019), 135-153. https://doi.org/10.4995/agt.2019.10474 es_ES
dc.relation.references J. Haarmann, M. P. Murphy, C. S. Peters and P. C. Staecker, Homotopy equivalence in finite digital images, Journal of Mathematical Imaging and Vision 53 (2015), 288-302. https://doi.org/10.1007/s10851-015-0578-8 es_ES
dc.relation.references B. Jiang, Lectures on Nielsen fixed point theory, Contemporary Mathematics 18 (1983). https://doi.org/10.1090/conm/014 es_ES
dc.relation.references E. Khalimsky, Motion, deformation, and homotopy in finite spaces, in Proceedings IEEE Intl. Conf. on Systems, Man, and Cybernetics (1987), 227-234. es_ES
dc.relation.references A. Rosenfeld, "Continuous" functions on digital pictures, Pattern Recognition Letters 4 (1986), 177-184. https://doi.org/10.1016/0167-8655(86)90017-6 es_ES
dc.relation.references P. C. Staecker, Some enumerations of binary digital images, arXiv:1502.06236, 2015. es_ES


This item appears in the following Collection(s)

Show simple item record