Let $X$ be a strictly $K$-analytic space and $L$ a line bundle on $X$. Then

1. i)

   the isometry classes of piecewise linear metrics on line bundles on $X$ form an abelian group with respect to $\otimes$.

2. ii)

   the pull-back $f^{\ast}\|\cdot\|$ of a piecewise linear metric $\|\cdot\|$ on $L$ with respect to a morphism $f:Y\rightarrow X$ of strictly $K$-analytic spaces is a piecewise linear metric on $f^{\ast}L$.

3. iii)

   the minimum and the maximum of two piecewise linear metrics on $L$ are again piecewise linear metrics on $L$.