Computably and punctually universal spaces

Computably and punctually universal spaces Full article

Journal

Annals of Pure and Applied Logic
ISSN: 0168-0072

Output data

Year: 2025, Volume: 176, Number: 1, Article number : 103491, Pages count : 31 DOI: 10.1016/j.apal.2024.103491

Tags

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

Authors

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

Affiliations

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

Funding (2)

1	Mathematical Center in Akademgorodok	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

Submitted:	Mar 19, 2022
Accepted:	Jun 26, 2024
Published online:	Jul 10, 2024
Published print:	Aug 7, 2024

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

DB	Citing
OpenAlex	3