A study of the quasi covering dimension for finite spaces through the matrix theory

Yıl 2017, Cilt: 46 Sayı: 1, 111 - 125, 01.02.2017

D. N. Georgiou A. C. Megaritis F. Sereti

Öz

We use matrices to study the dimension function dim$_q$, calling quasi covering dimension, for finite topological spaces, which is always greater
than or equal to the classical covering dimension dim. In particular, we present algorithms in order to compute the dim$_q(X)$ of an arbitrary finite topological space $X$.

Anahtar Kelimeler

Covering dimension, quasi covering dimension, quasi cover, dense set

Kaynakça

• Georgiou, D. N. and Megaritis, A. C. Covering dimension and finite spaces, Applied Math- ematics and Computation, 218 (2011), 31223130.
• Georgiou, D. N. and Megaritis, A. C. An algorithm of polynomial order for computing the covering dimension of a finite space, Applied Mathematics and Computation, 231 (2014), 276283.
• Engelking, R. Theory of dimensions, finite and infinite, Sigma Series in Pure Mathematics, 10. Heldermann Verlag, Lemgo, 1995. viii+401 pp.
• Eves, H. Elementary matrix theory, Reprint of the 1966 edition, Dover Books on Advanced Mathematics, Dover Publications, Inc., New York, 1980. xvi+325 pp.
• Georgiou, D. N., Megaritis, A. C. and Sereti, F. A topological dimension greater than or equal to the classical covering dimension, accepted for publication in Houston Journal of Mathematics.
• Pears, A. R. Dimension Theory of General Spaces, Cambridge University Press, Cambridge, England-New York-Melbourne, 1975. xii+428 pp.
• Shiraki, M. On finite topological spaces, Rep. Fac. Sci. Kagoshima Univ. 1 1968 18.