Some non-multiplicative properties are $l$-invariant

summary:A cardinal function $\varphi$ (or a property $\Cal P$) is called $l$-invariant if for any Tychonoff spaces $X$ and $Y$ with $C_p(X)$ and $C_p(Y)$ linearly homeomorphic we have $\varphi(X)=\varphi(Y)$ (or the space $X$ has $\Cal P$ ($\equiv X\vdash {\Cal P}$) iff $Y\vdash\Cal P$). We prove that the hereditary Lindelöf number is $l$-invariant as well as that there are models of $ZFC$ in which hereditary separability is $l$-invariant