Relative dimension r-dim and finite spaces

• Megaritis, A.C. ^[1]
  1. [1] Technological Educational Institute of Messolonghi

     Technological Educational Institute of Messolonghi

     Dimos Missolonghi, Grecia

     
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 13, Nº. 1, 2012, págs. 91-102
• Idioma: inglés
• DOI: 10.4995/agt.2012.1641
• Enlaces
  • Texto completo
• Resumen

  • 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.

• Referencias bibliográficas
  • 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...
  • 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.