JOURNAL BROWSE
Search
Advanced SearchSearch Tips
COMMUTATIVE MONOID OF THE SET OF k-ISOMORPHISM CLASSES OF SIMPLE CLOSED k-SURFACES IN Z3
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
  • Journal title : Honam Mathematical Journal
  • Volume 32, Issue 1,  2010, pp.141-155
  • Publisher : The Honam Mathematical Society
  • DOI : 10.5831/HMJ.2010.32.1.141
 Title & Authors
COMMUTATIVE MONOID OF THE SET OF k-ISOMORPHISM CLASSES OF SIMPLE CLOSED k-SURFACES IN Z3
Han, Sang-Eon;
  PDF(new window)
 Abstract
In this paper we prove that with some hypothesis the set of k-isomorphism classes of simple closed k-surfaces in forms a commutative monoid with an operation derived from a digital connected sum, k {18,26}. Besides, with some hypothesis the set of k-homotopy equivalence classes of closed k-surfaces in is also proved to be a commutative monoid with the above operation, k {18,26}.
 Keywords
digital k-graph;digital k-surface;-isomorphism;digital connected sum k-homotopy equivalence;k-contractibility;simple closed k-surface;(commutative) monoid;
 Language
English
 Cited by
 References
1.
G. Bertrand and M. Malgouyres, Some topological properties of discrete surfaces, Jour. of Mathematical Imaging and Vision, 11 (1999) 207-221. crossref(new window)

2.
L. Boxer, Digitally continuous functions Pattern Recognition Letters 15 (1994) 833-839. crossref(new window)

3.
L. Boxer, A classical construction for the digital fundamental group, Jour. of Mathematical Imaging and Vision. 10 (1999) 51-62. crossref(new window)

4.
L. Boxer, Properties of digital homotopy, Jour. of Mathematical Imaging and Vision 22 (2005) 19-26. crossref(new window)

5.
A.I. Bykov, L.G. Zerkalov, M.A. Rodriguez Pineda, Index of a point of 3-D digital binary image and algorithm of computing its Euler characteristic, Pattern Recognition 32 (1999) 845-850. crossref(new window)

6.
L. Chen, Discrete Surfaces and Manifolds, Scientific and Practical Computing, 2004.

7.
A,V. Evako, Topological properties of closed digital spaces: One method of constructing digital models of closed continuous surfaces by using covers, Computer Vision and Image Understanding, 102 (2006) 134-144. crossref(new window)

8.
S.E. Han, Computer topology and its applications, Honam Math. Jour., 25(1) (2003) 153-162.

9.
S.E. Han, Connected sum of digital closed surfaces, Information Sciences 116 (3)(2006) 332-348.

10.
S.E. Han, Discrete Homotopy of a Closed k-Surface, IWCIA 2006 LNCS 4040, Springer-Verlag Berlin, pp.214-225, 2006.

11.
S.E. Han, Minimal digital pseudotorus with k-adjacency, Honam Mathematical Journal 26(2) (2004) 237-246.

12.
S.E. Han, Non-product property of the digital fundamental group, Information Sciences 171 (1-3) (2005) 73-91. crossref(new window)

13.
S.E. Han, On the simplicial complex stemmed from a digital graph, Honam Mathematical Journal 27 (1) (2005) 115-129.

14.
S.E. Han, Minimal simple closed 18-surfeces and a topological preservation of 3D surfaces, Information Sciences 176(2)(2006) 120-134. crossref(new window)

15.
S.E. Han, Digital fundamental group and Euler characteristic of a connected sum of digital dosed surfaces, Information Sciences 177(16)(2007) 3314-3326. crossref(new window)

16.
S.E. Han, Strong k-deformation retract and its applications, Journal of the Korean Mathematical Society 44(6)(2007) 1479-1503. crossref(new window)

17.
S.E. Han, Comparison among digital fundamental groups and its applications, Information Sciences 178(2008) 2091-2104 . crossref(new window)

18.
S.E. Han, Equivalent ($k_0$, $k_1$)-covering and generalized digital lifting, Information Sciences 178 (2) (2008) 550-561. crossref(new window)

19.
S.E. Han, The k-homotopic thinning and a torus-like digital image in Z", Journal of Mathematical Imaging and Vision 31 (1) (2008) 1-16. crossref(new window)

20.
S.E. Han, Remark on a generalized universal covering space, Honam Mathematical Jour 31(3)(2009) 267-278. crossref(new window)

21.
S.E. Han, Existence problem of a generalized universal covering space, Acta Applicandae Mathematicae 109(3)(2010) 805-827. crossref(new window)

22.
G. T. Herman, Oriented surfaces in digital spaces, CVGIP: Graphical Models and Image Processing 55 (1993) 381-396. crossref(new window)

23.
In-Soo Kim, S.E. Han, Digital covering theory and its application, Honam Math. Jour. 30 (4)(2008) 589-602. crossref(new window)

24.
In-Soo Kim, S.E. Han, C.J. Yoo, The pasting property of digital continuity, Acta Applicandae Mathematicae (2009), doi 10.1007/s10440-008-9422-0, On line first publication . crossref(new window)

25.
R. Klette, A. Rosenfeld, Digital Geometry, Morgan Kaufmann, San Francisco, 2004

26.
T.Y. Kong, A. Rosenfeld, Topological Algorithms for the Digital Image Processing, Elsevier Science, Amsterdam, 1996.

27.
D.G. Morgenthaler, A. Rosenfeld, Surfaces in three dimensional digital images, Information and Control, 51 (1981) 227-247. crossref(new window)

28.
A. Rosenfeld, Digital topology, Am. Math. Mon. 86 (1979) 76-87.