On a class of homeomorphisms of function spaces preserving the Lindelöf number of domains | Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika – Tomsk State University Journal of Mathematics and Mechanics. 2023. № 86. DOI: 10.17223/19988621/86/12

On a class of homeomorphisms of function spaces preserving the Lindelöf number of domains

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 Lindelof numbers l(X) and l(Y) are equal. This result generalizes the known theorem of A. Bouziad for linear homeomorphisms of function spaces.

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Keywords

Lindelof number, function space, pointwise convergence topology, finite support property

Authors

Name	Organization	E-mail
Lazarev Vadim R.	Tomsk State University	lazarev@math.tsu.ru

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References

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