Relative dimension r-dim and finite spaces

Authors

  • A.C. Megaritis Technological Educational Institute of Messolonghi

DOI:

https://doi.org/10.4995/agt.2012.1641

Keywords:

Covering dimension, Relative dimension, Finite space, Incidence matrix

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.

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Author Biography

A.C. Megaritis, Technological Educational Institute of Messolonghi

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

References

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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

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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.

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Published

2012-04-15

How to Cite

[1]
A. Megaritis, “Relative dimension r-dim and finite spaces”, Appl. Gen. Topol., vol. 13, no. 1, pp. 91–102, Apr. 2012.

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Section

Articles