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Sequential decreasing strong size properties

  • Féelix Capulín EMAIL logo , Miguel A. Lara and Fernando Orozco-Zitli
Published/Copyright: October 20, 2018
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 68 Issue 5

Abstract

Let X be a continuum. The n-fold hyperspace Cn(X), n < ∞, is the space of all nonempty closed subsets of X with at most n components. A topological property P is said to be a (an almost) sequential decreasing strong size property provided that if μ is a strong size map for Cn(X, {tj}j=1∞ is a sequence in the interval (t,1) such that lim tj = t ∈ [0,1) (t ∈ (0,1)) and each fiber μ−1(tj) has property P, then so does μ−1(t). In this paper we show that the following properties are sequential decreasing strong size properties: being a Kelley continuum, local connectedness, continuum chainability and, unicoherence. Also we prove that indecomposability is an almost sequential decreasing strong size property.

MSC 2010: Primary 54C05, 54C10, 54B20; Secondary 54B15
Keywords: n-fold hyperspace; strong size property; strong size map; Kelley continuum; indecomposability; local connectedness; continuum chainability and unicoherence

  1. Communicated by David Buhagiar

Acknowledgement

The authors thank the referee for the suggestions made that improve the paper.

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Received: 2016-10-14
Accepted: 2017-09-01
Published Online: 2018-10-20
Published in Print: 2018-10-25

© 2018 Mathematical Institute Slovak Academy of Sciences

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  6. Some results on abstract convexity of functions
  7. Remarks on b-Metric and metric-preserving functions
  8. Generalization of Ostrowski inequality for convex functions
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  11. Application of tan(φ(ξ)/2)-expansion method to burgers and foam drainage equations
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https://doi.org/10.1515/ms-2017-0176
Keywords for this article
n-fold hyperspace; strong size property; strong size map; Kelley continuum; indecomposability; local connectedness; continuum chainability and unicoherence

Articles in the same Issue

  1. Prof. RNDr. Beloslav Riečan, DrSc., Dr.h.c. *NOV. 10, 1936 – †AUG. 13, 2018
  2. On the n × n × n Rubik's Cube
  3. Congruences involving alternating harmonic sums modulo pαqβ
  4. On the proximity of large primes
  5. On the factorizations of cubic polynomials with the same discriminant modulo a prime
  6. Some results on abstract convexity of functions
  7. Remarks on b-Metric and metric-preserving functions
  8. Generalization of Ostrowski inequality for convex functions
  9. On microscopic sets and Fubini Property in all directions
  10. New subfamily of meromorphic multivalent starlike functions in circular domain involving q-differential operator
  11. Application of tan(φ(ξ)/2)-expansion method to burgers and foam drainage equations
  12. Approximate sentinels for diffusion phenomena with pollution
  13. Remarks on a semilinear system in ℝn motivated by difference equations
  14. Oscillation tests for difference equations with several non-monotone deviating arguments
  15. On the regularity of one-sided fractional maximal functions
  16. A note on a Banach’s fixed point theorem in b-rectangular metric space and b-metric space
  17. A note about Volterra operator
  18. Some reverse and numerical radius inequalities
  19. A class of four-dimensional CR submanifolds in six dimensional nearly Kähler manifolds
  20. Sequential decreasing strong size properties
  21. Approximation of Information Divergences for Statistical Learning with Applications
  22. Wigner's theorem for an infinite set
  23. A note on automorphisms of lie ideals in prime rings
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