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Some non-multiplicative properties are $$l$$-invariant. (English) Zbl 0886.54005
Summary: A cardinal function $$\varphi$$ (or a property $$\mathcal P$$) is called $$l$$-invariant if for any Tikhonov 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 $$\mathcal P(\equiv X \vdash \mathcal P)$$ iff $$Y\vdash \mathcal P$$). 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.

##### MSC:
 54A25 Cardinality properties (cardinal functions and inequalities, discrete subsets)
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