| Title:
|
Property of being semi-Kelley for the cartesian products and hyperspaces (English) |
| Author:
|
Castañeda-Alvarado, Enrique |
| Author:
|
Vidal-Escobar, Ivon |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
58 |
| Issue:
|
3 |
| Year:
|
2017 |
| Pages:
|
359-369 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
continuum |
| Keyword:
|
property of Kelley |
| Keyword:
|
semi-Kelley |
| Keyword:
|
cartesian products |
| Keyword:
|
hyperspaces |
| Keyword:
|
Whitney levels |
| MSC:
|
54B20 |
| MSC:
|
54F15 |
| MSC:
|
54G20 |
| idZBL:
|
Zbl 06837071 |
| idMR:
|
MR3708779 |
| DOI:
|
10.14712/1213-7243.2015.217 |
| . |
| Date available:
|
2017-11-22T09:24:15Z |
| Last updated:
|
2019-10-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/146909 |
| . |
| Reference:
|
[1] 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. Zbl 1302.54066, MR 3222532 |
| Reference:
|
[2] Charatonik J.J.: Semi-Kelley continua and smoothness.Questions Answers Gen. Topology 21 (2003), 103–108. Zbl 1041.54031, MR 1998212 |
| Reference:
|
[3] Charatonik J.J., Charatonik W.J.: A weaker form of the property of Kelley.Topology Proc. 23 (1998), 69–99. Zbl 0943.54022, MR 1743801 |
| Reference:
|
[4] Charatonik J.J., Charatonik W.J.: Property of Kelley for the cartesian product and hyperspaces.Proc. Amer. Math. Soc. 136 (2008), 341–346. MR 2350421, 10.1090/S0002-9939-07-08650-9 |
| Reference:
|
[5] 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. Zbl 0548.54004, MR 0770219 |
| Reference:
|
[6] Eberhat C., Nadler S.B., Jr.: The dimension of certain hyperspaces.Bull. Pol. Acad. Sci., 19 (1971), 1027–1034. MR 0303513 |
| Reference:
|
[7] Kato H.: A note on continuus mappings and the property of J.L. Kelley.Proc. Amer. Math. Soc. 112 (1991), 1143–1148. MR 1073527, 10.1090/S0002-9939-1991-1073527-4 |
| Reference:
|
[8] Kelley J.L.: Hyperspaces of a continuum.Trans. Amer. Math. Soc. 52 (1942), 22–36. Zbl 0061.40107, MR 0006505, 10.1090/S0002-9947-1942-0006505-8 |
| . |
