## Vladimir V. Tkachuk

*Some non-multiplicative properties are $l$\hskip 2pt-invariant *

Comment.Math.Univ.Carolinae 38,1 (1997) 169-175. **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

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