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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2017 / Cilt: 46 - Sayı: 1

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

D. N. GEORGIOU
A. C. MEGARİTİS
F. SERETİ
Sayfa
111–125
Yayın Tarihi
2022-10-18
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

In particular,we present algorithms in order to compute the dimq(X) of an arbitraryfinite topological space X.

📌 3 Maddede Bu Makale

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Amaç & Hipotez: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.
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Temel Bulgular & Veri: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.
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Sonuç & Katkı:In particular,we present algorithms in order to compute the dimq(X) of an arbitraryfinite topological space X.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri

Abstract

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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Bu Makaleye Atıf Yap

GEORGIOU, D. N., MEGARİTİS, A. C., SERETİ, F. (2022). A study of the quasi covering dimension for nite spaces through the matrix theory. Hacettepe Journal of Mathematics and Statistics, Cilt: 46 - Sayı: 1, 111–125. https://ajindex.com/articles/530007

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Kaynakça (4)

  1. Shiraki, M. On finite topological spaces, Rep. Fac. Sci. Kagoshima Univ. 1 1968 1-8.
  2. Pears, A. R. Dimension Theory of General Spaces, Cambridge University Press,
  3. 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 in nite, 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.
  4. Georgiou, D. N. and Megaritis, A. C. Covering dimension and nite spaces, Applied Mathematics and Computation, 218 (2011), 3122-3130.