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Variations of star selection principles on hyperspaces

  • Javier Casas-de la Rosa
Veröffentlicht/Copyright: 13. Mai 2024
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Mathematica Slovaca
Aus der Zeitschrift Mathematica Slovaca Band 74 Heft 1

Abstract

In this paper, we define some combinatorial principles to characterize spaces X whose hyperspace satisfies some variation of some classical star selection principle. Specifically, the variations characterized are the selective and absolute versions of the star selection principles for the Menger and Rothberger cases; also, the hyperspaces considered in these characterizations are CL(X), 𝕂(X), đ”œ(X) and ℂ𝕊(X) in both cases, endowed with either the Fell topology or the Vietoris topology.

MSC 2010: Primary 54B20; 54D20
Keywords: Hyperspaces; Fell topology; Vietoris topology; star selection principles; (absolutely) strongly star-Menger; (selectively) strongly star-Menger; (absolutely) strongly star-Rothberger; (selectively) strongly star-Rothberger

This work was supported by UNAM Posdoctoral Program (POSDOC).

Acknowledgement

The author thanks the referee for his/her careful reading of the paper.

  1. (Communicated by David Buhagiar)

References

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Received: 2023-01-27
Accepted: 2023-03-19
Published Online: 2024-05-13
Published in Print: 2024-02-26

© 2024 Mathematical Institute Slovak Academy of Sciences

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https://doi.org/10.1515/ms-2024-0013
Schlagwörter fĂŒr diesen Artikel
Hyperspaces; Fell topology; Vietoris topology; star selection principles; (absolutely) strongly star-Menger; (selectively) strongly star-Menger; (absolutely) strongly star-Rothberger; (selectively) strongly star-Rothberger

Artikel in diesem Heft

  1. Prof. RNDr. Gejza Wimmer, DrSc. – 3/4 C?
  2. On hyper (r, q)-Fibonacci polynomials
  3. The pointfree version of 𝓒c(X) via the ranges of functions
  4. On the x-coordinates of Pell equations that are products of two Pell numbers
  5. Subordination properties and coefficient problems for a novel class of convex functions
  6. Certain radii problems for 𝓱∗(ψ) and special functions
  7. On direct and inverse Poletsky inequalities with a tangential dilatation
  8. Fourth-order nonlinear strongly non-canonical delay differential equations: new oscillation criteria via canonical transform
  9. Hermite interpolation of type total degree associated with certain spaces of polynomials
  10. Decomposition in direct sum of seminormed vector spaces and Mazur–Ulam theorem
  11. A fixed point technique to the stability of Hadamard 𝔇-hom-der in Banach algebras
  12. Compact subsets of Cλ,u(X)
  13. Variations of star selection principles on hyperspaces
  14. On lower density operators
  15. Gröbner bases in the mod 2 cohomology of oriented Grassmann manifolds G͠2t,3
  16. On the von Bahr–Esseen inequality for pairwise independent random vectors in Hilbert spaces with applications to mean convergence
  17. Large deviations for some dependent heavy tailed random sequences
  18. Metric, stratifiable and uniform spaces of G-permutation degree
  19. In memory of Paolo
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