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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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