The Correspondence Between Graphs and Alexandroff Spaces

Authors

DOI:

https://doi.org/10.26713/cma.v14i1.2128

Keywords:

Graph, Spectral, Prime spectrum, Ring, Alexandroff space

Abstract

In this paper, we study the correspondence between graphs and Alexandroff spaces. It is shown that a topological space \(X\) is Alexandroff if and only if \(X\) is a graph equipped with the \(X\)-right topology.

Downloads

Download data is not yet available.

References

P. Alexandroff, Diskrete Räume, Matematicheskiy sbornik 2(44)(3) (1937), 501 – 518 (in Russian), URL: https://www.mathnet.ru/links/6e8bdefe22c4647aeff14e7ffe303da4/sm5579.pdf.

G. T. Herman, On topology as applied to image analysis, Computer Vision, Graphics, and Image Processing 52(3) (1990), 409 – 415, DOI: 10.1016/0734-189X(90)90084-9.

M. Hochster, Prime ideal structure in commutative rings, Transactions of the American Mathematical Society 142 (1969), 43 – 60, DOI: 10.1090/S0002-9947-1969-0251026-X.

I. Kaplansky, Commutative Rings, revised edition, The University of Chicago Press, Chicago and London (1974), URL: https://www.maths.ed.ac.uk/~v1ranick/papers/kaprings.pdf.

E. H. Kronheimer, The topology of digital images, Topology and its Applications 46(3) (1992), 279 – 303, DOI: 10.1016/0166-8641(92)90019-V.

W. J. Lewis and J. Ohm, The ordering of spec R, Canadian Journal of Mathematics 28(4) (1973), 820 – 835, DOI: 10.4153/CJM-1976-079-2.

K. H. Rosen, Discrete Mathematics and Its Applications, 7th edition, The McGraw-Hill (2012), URL: https://faculty.ksu.edu.sa/sites/default/files/rosen_discrete_mathematics_and_its_applications_7th_edition.pdf.

Downloads

Published

May 9, 2023

Citations

Issue

Section

Research Article

How to Cite

Harbi, B. A. (2023). The Correspondence Between Graphs and Alexandroff Spaces. Communications in Mathematics and Applications, 14(1), 451-457. https://doi.org/10.26713/cma.v14i1.2128