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Let $X$ be a continuum. In Proposition 31 of J.J. Charatonik and W.J. Charatonik, , Comment. Math. Univ. Carolin. (2000), no. 1, 123–132, it is claimed that $L\left(X\right)={\bigcap }_{p\in X}S\left(p\right)$, where $L\left(X\right)$ is the set of points at which $X$ is locally connected and, for $p\in X$, $a\in S\left(p\right)$ 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 $P\left(X\right)={\bigcap }_{p\in X}S\left(p\right)$, where $P\left(X\right)$ is the set of points at which $X$ is connected im kleinen. We also use the correct equality to obtain some results concerning...