Geodesic
On a class of homeomorphisms of function spaces preserving the Lindel\"of number of domains
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 86 (2023), pp. 159-166

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We consider the class of all homeomorphisms between the function spaces of the form $C_p(X)$, $C_p(Y)$ such that the images of $Y$ and $X$ under their dual and, respectively, inverse dual mappings consist of finitely supported functionals. We prove that if a homeomorphism belongs to this class, then Lindelöf numbers $l(X)$ and $l(Y)$ are equal. This result generalizes the known theorem of A. Bouziad for linear homeomorphisms of function spaces.
Keywords: Lindelöf number, function space, pointwise convergence topology, finite support property. 
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     author = {V. R. Lazarev},
     title = {On a class of homeomorphisms of function spaces preserving the {Lindel\"of} number of domains},
     journal = {Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika},
     pages = {159--166},
     publisher = {mathdoc},
     number = {86},
     year = {2023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VTGU_2023_86_a11/}
}
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V. R. Lazarev. On a class of homeomorphisms of function spaces preserving the Lindel\"of number of domains. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 86 (2023), pp. 159-166. http://geodesic.mathdoc.fr/item/VTGU_2023_86_a11/