Relative dimension r-dim and finite spaces

A.C. Megaritis

Greece

Technological Educational Institute of Messolonghi

Department of Accounting, Technological Educational Institute of Messolonghi, 30200 Messolonghi, Greece

Submitted: 2013-07-29

|

Accepted: 2013-07-29

|

Published: 2012-04-15

DOI: https://doi.org/10.4995/agt.2012.1641
Funding Data

Downloads

Keywords:

Covering dimension, Relative dimension, Finite space, Incidence matrix

Supporting agencies:

This research was not funded

Abstract:

In 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.
Show more Show less

References:

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 ∗ 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 ∗ 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.

Show more Show less