On a class of homeomorphisms of function spaces preserving the Lindelöf number of domains | Вестник Томского государственного университета. Математика и механика. 2023. № 86. DOI: 10.17223/19988621/86/12

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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 Cp(X), Cp(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.

Ключевые слова

число Линделёфа, пространство функций, топология поточечной сходимости, свойство конечного носителя

Авторы

ФИООрганизацияДополнительноE-mail
Лазарев Вадим РемировичТомский государственный университеткандидат физико-математических наук, доцент кафедры математического анализа и теории функций механико-математического факультетаlazarev@math.tsu.ru
Всего: 1

Ссылки

Bouziad A. (2001) Le degre de Lindelof est /-invariant. Proceedings of the American Mathe matical Society. 129(3). pp. 913-919.
Arbit A.V. (2008) The Lindelof number is /fu-invariant. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika - Tomsk State University Journal of Mathematics and Mechanics. 2(3). pp. 10-19.
Arbit A.V. (2011) The Lindelof number greater than continuum is fu-invariant. Serdica Mathematical Journal. 37. pp. 143-162.
Lazarev V.R. (2022) Functionals with a finite support and homeomorphisms of spaces of con tinuous functions. Proceedings of the International Scientific Conference LXXV Herzen Readings. Modern Problems of Mathematics and Mathematical Education, 2022. St. Petersburg. pp. 218-223.
Lazarev V.R. (2020) On the weak finite support property of homeomorphisms of function spaces on ordinals. Topology and Its Applications. 275. p. 107012. DOI: 10.1016/j.topol. 2019.107012.
Bessaga C., Pelczynski A. (1960) Spaces of continuous functions (IV). (On isomorphical clas sification of spaces of continuous functions). Studia Mathematica. 19(1). pp. 53-62.
Osipov A.V. (2020) Projective versions of the properties in the Scheepers Diagram. Topology and Its Applications. 278. p. 107232. DOI: 10.1016/j.topol.2020.107232.
On a class of homeomorphisms of function spaces preserving the Lindelöf number of domains | Вестник Томского государственного университета. Математика и механика. 2023. № 86. DOI: 10.17223/19988621/86/12

On a class of homeomorphisms of function spaces preserving the Lindelöf number of domains | Вестник Томского государственного университета. Математика и механика. 2023. № 86. DOI: 10.17223/19988621/86/12