| Title:
|
A note on the paper ``Smoothness and the property of Kelley'' (English) |
| Author:
|
Acosta, Gerardo |
| Author:
|
Aguilar-Martínez, Álgebra |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
48 |
| Issue:
|
4 |
| Year:
|
2007 |
| Pages:
|
669-676 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $X$ be a continuum. In Proposition 31 of J.J. Charatonik and W.J. Charatonik, {\it Smoothness and the property of Kelley\/}, Comment. Math. Univ. Carolin. {\bf 41} (2000), no. 1, 123--132, it is claimed that $L(X) = \bigcap _{p\in X}S(p)$, where $L(X)$ is the set of points at which $X$ is locally connected and, for $p\in X$, $a\in S(p)$ if and only if $X$ is smooth at $p$ with respect to $a$. In this paper we show that such equality is incorrect and that the correct equality is $P(X) = \bigcap _{p\in X}S(p)$, where $P(X)$ is the set of points at which $X$ is connected im kleinen. We also use the correct equality to obtain some results concerning the property of Kelley. (English) |
| Keyword:
|
connectedness im kleinen |
| Keyword:
|
continuum |
| Keyword:
|
hyperspace |
| Keyword:
|
local connectedness |
| Keyword:
|
property of Kelley |
| Keyword:
|
smoothness |
| MSC:
|
54B20 |
| MSC:
|
54F15 |
| MSC:
|
54F50 |
| idZBL:
|
Zbl 1199.54183 |
| idMR:
|
MR2375167 |
| . |
| Date available:
|
2009-05-05T17:05:32Z |
| Last updated:
|
2012-05-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119689 |
| . |
| Reference:
|
[1] Acosta G.: On smooth fans and unique hyperspace.Houston J. Math. 30 (2004), 99-115. MR 2048337 |
| Reference:
|
[2] Acosta G., Illanes A.: Continua which have the property of Kelley hereditarily.Topology Appl. 102 (2000), 151-162. Zbl 0940.54038, MR 1741483 |
| Reference:
|
[3] Charatonik J.J., Charatonik W.J.: Smoothness and the property of Kelley.Comment Math. Univ. Carolin. 41 1 (2000), 123-132. Zbl 1037.54506, MR 1756932 |
| Reference:
|
[4] Maćkowiak T.: On smooth continua.Fund. Math. 85 (1974), 79-95. MR 0365532 |
| Reference:
|
[5] Nadler S.B., Jr.: Hyperspaces of Sets.Marcel Dekker, Inc., New York and Basel, 1978. Zbl 1125.54001, MR 0500811 |
| Reference:
|
[6] Nadler S.B., Jr.: Continuum Theory.Marcel Dekker, Inc., New York, Basel and Hong Kong, 1992. Zbl 0819.54015, MR 1192552 |
| . |
