Relative dimension r-dim and finite spaces
Keywords:Covering dimension, Relative dimension, Finite space, Incidence matrix
AbstractIn a relative covering dimension is defined and studied which is denoted by r-dim. In this paper we give an algorithm of polynomial order for computing the dimension r-dim of a pair (Q,X), where Q is a subset of a finite space X, using matrix algebra.
P. Alexandroff, Diskrete Räume, Mat. Sb. (N.S.) 2 (1937), 501–518.
R. Engelking, Theory of dimensions, finite and infinite, Sigma Series in Pure Mathematics, 10. Heldermann Verlag, Lemgo, 1995. viii+401 pp.
H. Eves, Elementary matrix theory, Dover Publications, Inc., New York, 1980. xvi+325 pp.
D. N. Georgiou and A. C. Megaritis, On a New Relative Invariant Covering Dimension, Extracta Mathematicae 25, no. 3 (2010), 263–275.
D. N. Georgiou and A. C. Megaritis, Covering dimension and finite spaces, Applied Mathematics and Computation 218 (2011), 3122–3130. http://dx.doi.org/10.1016/j.amc.2011.08.040
D. N. Georgiou and A. C. Megaritis, On the relative dimensions dim and dim âˆ— I, Questions and Answers in General Topology 29 (2011), 1–16.
D. N. Georgiou and A. C. Megaritis, On the relative dimensions dim and dim âˆ— II, Questions and Answers in General Topology 29 (2011), 17–29.
M. Shiraki, On finite topological spaces, Rep. Fac. Sci. Kagoshima Univ. 1 1968 1-8.
J. Valuyeva, On relative dimension concepts, Questions Answers Gen. Topology 15, no. 1 (1997), 21–24.
How to Cite
This journal is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.