A study of new dimensions for ideal topological spaces

• Sereti, Fotini ^[1]
  1. [1] University of Western Macedonia

     University of Western Macedonia

     Dimos Kozani, Grecia

     
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 25, Nº. 1, 2024, págs. 183-198
• Idioma: inglés
• DOI: 10.4995/agt.2024.19760
• Enlaces
  • Texto completo
• Resumen

  • In this paper new notions of dimensions for ideal topological spaces are inserted, called *-quasi covering dimension and ideal quasicovering dimension. We study several of their properties and investigate their relations with types of covering dimensions like the *-covering dimension and the ideal covering dimension.

• Referencias bibliográficas
  • M. G. Charalambous, Dimension Theory, A Selection of Theorems and Counterexamples, Springer Nature Switzerland AG, Cham, Switzerland, 2019....
  • M. Coornaert, Topological dimension and dynamical systems, Translated and revised from the 2005 French original, Universitext, Springer, Cham,...
  • J. Dontchev, M. Ganster, D. Rose, Ideal resolvability, Topology and its Applications 93, no. 1 (1999), 1-16. https://doi.org/10.1016/S0166-8641(97)00257-5
  • R. Engelking, General Topology, Heldermann Verlag, Berlin, 1989.
  • R. Engelking, Theory of Dimensions, Finite and Infinite, Heldermann Verlag, Berlin, 1995.
  • D. N. Georgiou, A. C. Megaritis, Covering dimension and finite spaces, Applied Mathematics and Computation 218 (2014), 3122-3130. https://doi.org/10.1016/j.amc.2011.08.040
  • D. N. Georgiou, A. C. Megaritis, S. Moshokoa, Small inductive dimension and Alexandroff topological spaces, Topology and its Applications...
  • D. N. Georgiou, A. C. Megaritis, F. Sereti, A study of the quasi covering dimension for finite spaces through matrix theory, Hacettepe Journal...
  • D. N. Georgiou, A. C. Megaritis, F. Sereti, A study of the quasi covering dimension of Alexandroff countable spaces using matrices, Filomat...
  • D. N. Georgiou, A. C. Megaritis, F. Sereti, A topological dimension greater than or equal to the classical covering dimension, Houston Journal...
  • T. R. Hamlett, D. Rose, D. Janković, Paracompactness with respect to an ideal, Internat. J. Math. Math. Sci. 20, no. 3 (1997), 433-442. https://doi.org/10.1155/S0161171297000598
  • D. Janković, T. R. Hamlett, New topologies from old via ideals, Amer. Math. Monthly 97, no. 4 (1990), 295-310. https://doi.org/10.1080/00029890.1990.11995593
  • K. Kuratowski, Topologie I, Monografie Matematyczne 3, Warszawa-Lwów, 1933.
  • A. C. Megaritis, Covering dimension and ideal topological spaces, Quaestiones Mathematicae 45, no. 2 (2022), 197-212. https://doi.org/10.2989/16073606.2020.1851309
  • K. Nagami, Dimension theory, Pure and Applied Mathematics, vol. 37 Academic Press, New York-London, 1970.
  • J. Nagata, Modern dimension theory, Revised edition, Sigma Series in Pure Mathematics, 2, Heldermann Verlag, Berlin, 1983.
  • A. R. Pears, Dimension theory of general spaces, Cambridge University Press, Cambridge, 1975.
  • F. Sereti, Small and large inductive dimension for ideal topological spaces, Applied General Topology 22, no. 2 (2021), 417-434. https://doi.org/10.4995/agt.2021.15231