The Marcus Topology Coincides with the Quotient of Slapal's Topology

Annie kurien K; M.S.Samuel

doi:https://doi.org/10.14445/22315373/IJMTT-V62P526

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 62 | Number 3 | Year 2018 | Article Id. IJMTT-V62P526 | DOI : https://doi.org/10.14445/22315373/IJMTT-V62P526

The Marcus Topology Coincides with the Quotient of Slapal's Topology

Annie kurien K, M.S.Samuel

Abstract

In this paper we study properties of Marcus topology and Slapal’s topology and the relation between them.

Keywords

Marcus topology, Slapal’s topology, quotient topology, 8-adjacent, 4- adjacent, T1/2-topology.

References

[1] Ulrich Echhardt and Longen J. Lalicki. Topologies for the digital spaces Z2 and Z3. Computer Vision and Image Understanding, 90:295–312, 2003.
[2] Gabor T. Herman. Geometry of digital spaces. Birkhauser, 1998.
[3] E. D. Khalimsky, R. Kopperman, and P. R. Meyer. Computer graphics and connected topologies on finite ordered sets. Topology Appl., 36:1–17, 1990.
[4] J. Slapal. Closure operations for digital topology. Theor. Comp. Sci., 305:457–471, 2003.
[5] J. Slapal. Digital Jordan curves. Topology Appl., 153(17):3255–3264, 2006.

Citation :

Annie kurien K, M.S.Samuel, "The Marcus Topology Coincides with the Quotient of Slapal's Topology," International Journal of Mathematics Trends and Technology (IJMTT), vol. 62, no. 3, pp. 184-187, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V62P526