On a linear homeomorphism of spaces of continuousfunctions on subsets of the Sorgenfrey line | Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika – Tomsk State University Journal of Mathematics and Mechanics. 2012. № 2(18).

On a linear homeomorphism of spaces of continuousfunctions on subsets of the Sorgenfrey line

In this paper, it isproved that the spaces Cp(I) and Cp(E) are linearly homeomorphic. Here, the interval I = [0,1] anda Cantor set E are equipped with the Sorgenfrey topology.

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Keywords

топология Зоргенфрея, пространства непрерывных функций, линейный гомеоморфизм, дополняемое подпространство, Sorgenfrey topology, spaces of continuous functions, linear homeomorphism, complemented subspace

Authors

Name	Organization	E-mail
Trofimenko Nadezhda Nikolaevna	National Research Tomsk State University	Trofimenko@sibmail.com
Khmyleva Tatiana Evgenievna	National Research Tomsk State University	vestnik tgu mm@math.tsu.ru

Всего: 2

References

Pestov V.G. The coincidence of the dimensions dim of l-equivalent topological spaces // Dokl. Akad. Nauk SSSR. 1982. No. 266. P. 553-556.

Куратовский К., Мостовский А. Теория множеств. М.: Мир, 1970. 416 с.

Kalton N.J., Albiac F. Topics in Banach Space Theory. Springer, 2006. 373 р.

Архангельский А.В. О линейных гомеоморфизмах пространств функций // ДАН СССР. 1982. Т. 264. № 6. С. 1289-1292.