On linear homeomorphisms of spaces of continuous functions with the pointwise convergence topology | Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika – Tomsk State University Journal of Mathematics and Mechanics. 2024. № 92. DOI: 10.17223/19988621/92/4

On linear homeomorphisms of spaces of continuous functions with the pointwise convergence topology

By analogy with the spaces Cp(X), we introduce into consideration the spaces Cp,A(X) of continuous realvalued functions with the topology of pointwise convergence on an everywhere dense subset A ⊂ X . For the spaces Cp,A [a,b] and Cp,B [c,d], where A=[a,b]\{a1,a2,....an}, and B = [c,d]\{b1,b2,....bm}, it is proved that the spaces Cp,A [a,b] and Cp,B [c,d] are linearly homeomorphic if and only if n = m.

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Keywords

Stieltjes integral, function of bounded variation, linearly bounded functionals, pointwise convergence topology, homeomorphism, continuous functions

Authors

Name	Organization	E-mail
Khmyleva Tatiana E.	Tomsk State University	tex2150@yandex.ru
Petrova Kira M.	Tomsk State University	lililitiy534@yandex.ru

Всего: 2

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