Property of being semi-Kelley for the cartesian products and hyperspaces
Enrique Castañeda-Alvarado; Ivon Vidal-Escobar
Commentationes Mathematicae Universitatis Carolinae (2017)
- Volume: 58, Issue: 3, page 359-369
- ISSN: 0010-2628
Access Full Article
top
Abstract
topHow to cite
topCastañeda-Alvarado, Enrique, and Vidal-Escobar, Ivon. "Property of being semi-Kelley for the cartesian products and hyperspaces." Commentationes Mathematicae Universitatis Carolinae 58.3 (2017): 359-369. <http://eudml.org/doc/294130>.
@article{Castañeda2017,
abstract = {In this paper we construct a Kelley continuum $X$ such that $X\times [0,1]$ is not semi-Kelley, this answers a question posed by J.J. Charatonik and W.J. Charatonik in A weaker form of the property of Kelley, Topology Proc. 23 (1998), 69–99. In addition, we show that the hyperspace $C(X)$ is not semi- Kelley. Further we show that small Whitney levels in $C(X)$ are not semi-Kelley, answering a question posed by A. Illanes in Problemas propuestos para el taller de Teoría de continuos y sus hiperespacios, Queretaro, 2013.},
author = {Castañeda-Alvarado, Enrique, Vidal-Escobar, Ivon},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {continuum; property of Kelley; semi-Kelley; cartesian products; hyperspaces; Whitney levels},
language = {eng},
number = {3},
pages = {359-369},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Property of being semi-Kelley for the cartesian products and hyperspaces},
url = {http://eudml.org/doc/294130},
volume = {58},
year = {2017},
}
TY - JOUR
AU - Castañeda-Alvarado, Enrique
AU - Vidal-Escobar, Ivon
TI - Property of being semi-Kelley for the cartesian products and hyperspaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2017
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 58
IS - 3
SP - 359
EP - 369
AB - In this paper we construct a Kelley continuum $X$ such that $X\times [0,1]$ is not semi-Kelley, this answers a question posed by J.J. Charatonik and W.J. Charatonik in A weaker form of the property of Kelley, Topology Proc. 23 (1998), 69–99. In addition, we show that the hyperspace $C(X)$ is not semi- Kelley. Further we show that small Whitney levels in $C(X)$ are not semi-Kelley, answering a question posed by A. Illanes in Problemas propuestos para el taller de Teoría de continuos y sus hiperespacios, Queretaro, 2013.
LA - eng
KW - continuum; property of Kelley; semi-Kelley; cartesian products; hyperspaces; Whitney levels
UR - http://eudml.org/doc/294130
ER -
References
top- Calderón-Camacho I.D., Castañeda-Alvarado E., Islas-Moreno C., Maya-Escudero D., Ruiz-Montañez F.J., Being semi-Kelley does not imply semi-smoothness, Questions Answers Gen. Topology 32 (2014), 73–77. Zbl1302.54066MR3222532
- Charatonik J.J., Semi-Kelley continua and smoothness, Questions Answers Gen. Topology 21 (2003), 103–108. Zbl1041.54031MR1998212
- Charatonik J.J., Charatonik W.J., A weaker form of the property of Kelley, Topology Proc. 23 (1998), 69–99. Zbl0943.54022MR1743801
- Charatonik J.J., Charatonik W.J., 10.1090/S0002-9939-07-08650-9, Proc. Amer. Math. Soc. 136 (2008), 341–346. MR2350421DOI10.1090/S0002-9939-07-08650-9
- Charatonik W.J., On the property of Kelley in hyperspaces, Topology Proc. International Conference, Leningrand 1982, Lectures Notes in Math., 1060, Springer, Berlin, 1984, pp. 7–10. Zbl0548.54004MR0770219
- Eberhat C., Nadler S.B., Jr., The dimension of certain hyperspaces, Bull. Pol. Acad. Sci., 19 (1971), 1027–1034. MR0303513
- Kato H., 10.1090/S0002-9939-1991-1073527-4, Proc. Amer. Math. Soc. 112 (1991), 1143–1148. MR1073527DOI10.1090/S0002-9939-1991-1073527-4
- Kelley J.L., 10.1090/S0002-9947-1942-0006505-8, Trans. Amer. Math. Soc. 52 (1942), 22–36. Zbl0061.40107MR0006505DOI10.1090/S0002-9947-1942-0006505-8
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.