Geodesic
Some non-multiplicative properties are $l$-invariant
Commentationes Mathematicae Universitatis Carolinae, Tome 38 (1997) no. 1, pp. 169-175

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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.
Classification : 54A25, 54A35, 54C35
Keywords: $l$-equivalent spaces; $l$-invariant property; hereditary Lindelöf number 
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Tkachuk, Vladimir V. Some non-multiplicative properties are $l$-invariant. Commentationes Mathematicae Universitatis Carolinae, Tome 38 (1997) no. 1, pp. 169-175. http://geodesic.mathdoc.fr/item/CMUC_1997__38_1_a15/