Geodesic
A note on the paper ``Smoothness and the property of Kelley''
Commentationes Mathematicae Universitatis Carolinae, Tome 48 (2007) no. 4, pp. 669-676

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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.
Classification : 54B20, 54F15, 54F50
Keywords: connectedness im kleinen; continuum; hyperspace; local connectedness; property of Kelley; smoothness 
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     author = {Acosta, Gerardo and Aguilar-Mart{\'\i}nez, \'Algebra},
     title = {A note on the paper {``Smoothness} and the property of {Kelley''}},
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Acosta, Gerardo; Aguilar-Martínez, Álgebra. A note on the paper ``Smoothness and the property of Kelley''. Commentationes Mathematicae Universitatis Carolinae, Tome 48 (2007) no. 4, pp. 669-676. http://geodesic.mathdoc.fr/item/CMUC_2007__48_4_a9/