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

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

We use matrices to study the dimension function dimq, calling quasicovering dimension, for finite topological spaces, which is always greaterthan or equal to the classical covering dimension dim. In particular,we present algorithms in order to compute the dimq(X) of an arbitraryfinite topological space X.

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  • Shiraki, M. On finite topological spaces, Rep. Fac. Sci. Kagoshima Univ. 1 1968 1-8.
  • Pears, A. R. Dimension Theory of General Spaces, Cambridge University Press, Cambridge, England-New York-Melbourne, 1975. xii+428 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.
  • Eves, H. Elementary matrix theory, Reprint of the 1966 edition, Dover Books on Advanced Mathematics, Dover Publications, Inc., New York, 1980. xvi+325 pp.
  • Engelking, R. Theory of dimensions, nite and innite, Sigma Series in Pure Mathematics, 10. Heldermann Verlag, Lemgo, 1995. viii+401 pp.
  • Georgiou, D. N. and Megaritis, A. C. An algorithm of polynomial order for computing the covering dimension of a nite space, Applied Mathematics and Computation, 231 (2014), 276-283.
  • Georgiou, D. N. and Megaritis, A. C. Covering dimension and nite spaces, Applied Mathematics and Computation, 218 (2011), 3122-3130.