Corollary

Let X be a topological space and let $x,y,z$ be points of X. The mappings $c\mapsto \overline{c}$ of $\Lambda_{x,y}(X)$ into $\Lambda_{y,x}(X)$ and $(c, d)\mapsto$ $c*d$ of $\Lambda_{x,y}(X)\times \Lambda_{y,z}(X)$ into $\Lambda_{x,z}(X)$ are continuous.