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$l$-equivalent spaces; $l$-invariant property; hereditary Lindelöf number
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.
[1] Arhangel'skii A.V.: Structure and classification of topological spaces and cardinal invariants (in Russian). Uspehi Mat. Nauk 33 6 (1978), 29-84. MR 0526012
[2] Arhangel'skii A.V.: On relationship between the invariants of topological groups and their subspaces (in Russian). Uspehi Mat. Nauk 35 3 (1980), 3-22. MR 0580615
[3] Arhangel'skii A.V.: Topological function spaces (in Russian). Moscow University Publishing House, Moscow, 1989. MR 1017630
[4] Arhangel'skii A.V.: $C_p$-theory. in: Recent Progress in General Topology, edited by J. van Mill and M. Hušek, North Holland, 1992, pp.1-56. MR 1229121 | Zbl 0932.54015
[5] Arhangel'skii A.V., Ponomarev V.I.: General Topology in Problems and Exercises (in Russian). Nauka Publishing House, Moscow, 1974. MR 0239550
[6] Engelking R.: General Topology. PWN, Warszawa, 1977. MR 0500780 | Zbl 0684.54001
[7] Gul'ko S.P., Khmyleva T.E.: The compactness is not preserved by $t$-equivalence (in Russian). Mat. Zametki 39 6 (1986), 895-903. MR 0855937
[8] Pestov V.G.: Some topological properties are preserved by $M$-equivalence (in Russian). Uspehi Mat. Nauk 39 6 (1984), 203-204. MR 0771108
[9] Tkachuk V.V.: On a method of constructing examples of $M$-equivalent spaces (in Russian). Uspehi Mat. Nauk 38 6 (1983), 127-128. MR 0728737
[10] Todorčević S.: Forcing positive partition relations. Trans. Amer. Math. Soc. 280 2 (1983), 703-720. MR 0716846
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