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Computably and punctually universal spaces Научная публикация

Журнал

Annals of Pure and Applied Logic
ISSN: 0168-0072

Вых. Данные

Год: 2025, Том: 176, Номер: 1, Номер статьи : 103491, Страниц : 31 DOI: 10.1016/j.apal.2024.103491

Ключевые слова

Universal spaces, Punctual, Computable Polish spacem Continuous functions on the unit intervalm Primitive recursive analysis

Авторы

Bagaviev Ramil ¹ , Batyrshin Ilnur I. ¹ , Bazhenov Nikolay ² , Bushtets Dmitry ³ , Dorzhieva Marina ³ , Koh Heer Tern ⁵ , Kornev Ruslan ^2,3 , Melnikov Alexander G. ⁴ , Ng Keng Meng ⁵

Организации

1	Kazan Federal University
2	Sobolev Institute of Mathematics
3	Novosibirsk State University
4	Victoria University of Wellington
5	Nanyang Technological University

Информация о финансировании (2)

1	Математический центр в Академгородке	075-15-2022-282
2	НОМЦ Приволжского федерального округа	075-02-2024-1438

We prove that the standard computable presentation of the space C[0, 1] of continuous real-valued functions on the unit interval is computably and punctually (primitively recursively) universal. From the perspective of modern computability theory, this settles a problem raised by Sierpiński in the 1940s. We prove that the original Urysohn’s construction of the universal separable Polish space Uis punctually universal. We also show that effectively compact, punctual Stone spaces are punctually homeomorphically embeddable into Cantor space 2ω; note that we do not require effective compactness be primitive recursive. We also prove that effective compactness cannot be dropped from the premises by constructing a counterexample.

Bagaviev R. , Batyrshin I.I. , Bazhenov N. , Bushtets D. , Dorzhieva M. , Koh H.T. , Kornev R. , Melnikov A.G. , Ng K.M.
Computably and punctually universal spaces
Annals of Pure and Applied Logic. 2025. V.176. N1. 103491 :1-31. DOI: 10.1016/j.apal.2024.103491 WOS Scopus OpenAlex

Поступила в редакцию:	19 мар. 2022 г.
Принята к публикации:	26 июн. 2024 г.
Опубликована online:	10 июл. 2024 г.
Опубликована в печати:	7 авг. 2024 г.

Web of science:	WOS:001291751200001
Scopus:	2-s2.0-85200913507
OpenAlex:	W4400487221

БД	Цитирований
OpenAlex	3