Local compactness and homeomorphisms of spaces ofcontinuous functions
In this paper we prove that 1) the spaces CP(S) and CP(T) of all continuous functions in the topology of pointwise convergence are not linearly homeomorphic if S, T are not locally compact metrizable while the derivation set T is compact and the derivation set S is not; 2) the spaces CK(X) and CK(Y) of all continuous functions in the compact-open topology are not homeomorphic if X and Y are completely regular spaces while X is locally compact and σ-compact and there is a point y0 Y of countable character such that every neighborhood of it is not a pseudocompact.
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Keywords
compact-open topology, topology of pointwise convergence, locally compact space, metrizable space, homeomorphism, linear homeomorphism, spaces of all continuous functions, компактно-открытая топология, топология поточечной сходимости, локально компактное пространство, метризуемое пространство, гомеоморфизм, линейный гомеоморфизм, пространства непрерывных функцийAuthors
| Name | Organization | |
| Khmyleva Т.Е. | vestnik_tgu_mm@math.tsu.ru | |
| Kirienko А.Е. | kirienko7@sibmail.com |
References
Архангельский A.B. Топологические пространства функций. М.: МГУ, 1989. 222 с.
Гулько С.П., Окунев О.Г. Локальная компактность и М-эквивалентность // Вопросы геометрии и топологии. Петрозаводск, 1986. С. 14-23.
Энгелькинг Р. Общая топология. М.: Мир, 1986. 752 с.
