Revista Integración, temas de matemáticas.

Revista Integración, temas de matemáticas

Vol. 38 No. 1 (2020): Revista Integración, temas de matemáticas
Research and Innovation Articles

On the property of Kelley for Hausdorff continua

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  • Mauricio Chacón-Tirado,
  • María de J. López
Mauricio Chacón-Tirado
Benemérita Universidad Autónoma de Puebla, Facultad de Ciencias Físico Matemáticas, Puebla, México.
María de J. López
Benemérita Universidad Autónoma de Puebla, Facultad de Ciencias Físico Matemáticas, Puebla, México.
DOI: https://doi.org/10.18273/revint.v38n1-2020005

Published 2020-01-24

Keywords

  • Continuum,
  • hyperspace,
  • maximal limit continuum,
  • property of Kelley,
  • strong maximal limit continuum

How to Cite

Chacón-Tirado, M., & López, M. de J. (2020). On the property of Kelley for Hausdorff continua. Revista Integración, Temas De matemáticas, 38(1), 55–66. https://doi.org/10.18273/revint.v38n1-2020005

Abstract

We introduce the concepts Hausdorff maximal limit continuum
and Hausdorff strong maximal limit continuum, for Hausdorff continua; these
definitions extend the concepts of maximal limit continuum and strong maximal
limit continuum, respectiveley, introduced by J. J. Charatonik and W.
J. Charatonik in 1998 for metric continua [1, Definitions 2.2 and 2.3]. We
show that in metric continua, being a maximal limit continuum is equivalent
to being a Hausdorff maximal limit continuum. We also show that in metric
continua, being a strong maximal limit continuum implies being a Hausdorff
strong maximal limit continuum. Finally, we show an equivalence of having
the property of Kelley, in terms of these new definitions, whose analog version
for metric continua was given by J. J. Charatonik and W. J. Charatonik.

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References

[1] Charatonik J.J. and Charatonik W. J., “A weaker form of the property of Kelley”, Topology
Proc. 23 (1998), 69–99.

[2] Charatonik W.J., “A homogeneous continuum without the property of Kelley”, Topology
Appl. 96 (1999), No. 3, 209–216.

[3] Illanes A. and Nadler, Jr. S. B., Hyperspaces Fundamentals and Recent Advances. Monographs
and Textbooks in Pure and Applied Math., Vol. 216, Marcel Dekker, Inc., New
York, 1999.

[4] Kelley J. L., “Hyperspaces of a continuum”, Trans. Amer. Math. Soc. 52 (1942), 22–36.

[5] Kelley J. L., General Topology. D. Van Nostrand Co., Inc., Princeton, New Jersey, 1960.

[6] Macías S., “On Jones’ set function T and the property of Kelley for Hausdorff continua”,
Topology Appl. 226 (2017), 51–65.

[7] Macías S., “Hausdorff continua and the uniform property of Effros”, Topology Appl. 230
(2017), 338–352.

[8] Macías S., “The property of Kelley and continua”, Rev. Integr. temas mat. 37 (2019), No.
1, 17–29.

[9] Makuchowski W., “On local connectedness in hyperspaces”, Bull. Polish Acad. Sci. Math.
47 (1999), No. 2, 119–126.

[10] McWaters M., “Arcs, semigroups, and hyperspaces”, Canadian J. Math. 20 (1968), 1207–
1210.

[11] Michael E., “Topologies on spaces of subsets”, Trans. Amer. Math. Soc. 71 (1951), 152–182.

[12] Mrówka S., “On the convergence of nets of sets”, Fund. Math. 45 (1958), 237–246.