Abstract: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 Lindel\"of number is $l$-invariant as well as that there are models of $ZFC$ in which hereditary separability is $l$-invariant.
Keywords: $l$-equivalent spaces, $l$-invariant property, hereditary Lindel\"of number
AMS Subject Classification: 54A25