Standard

Computably and punctually universal spaces. / Bagaviev, Ramil; Batyrshin, Ilnur I.; Bazhenov, Nikolay и др.

в: Annals of Pure and Applied Logic, Том 176, № 1, 103491, 01.2025.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

Harvard

Bagaviev, R, Batyrshin, II, Bazhenov, N, Bushtets, D, Dorzhieva, M, Koh, HT, Kornev, R, Melnikov, AG & Ng, KM 2025, 'Computably and punctually universal spaces', Annals of Pure and Applied Logic, Том. 176, № 1, 103491. https://doi.org/10.1016/j.apal.2024.103491

APA

Bagaviev, R., Batyrshin, I. I., Bazhenov, N., Bushtets, D., Dorzhieva, M., Koh, H. T., Kornev, R., Melnikov, A. G., & Ng, K. M. (2025). Computably and punctually universal spaces. Annals of Pure and Applied Logic, 176(1), [103491]. https://doi.org/10.1016/j.apal.2024.103491

Vancouver

Bagaviev R, Batyrshin II, Bazhenov N, Bushtets D, Dorzhieva M, Koh HT и др. Computably and punctually universal spaces. Annals of Pure and Applied Logic. 2025 янв.;176(1):103491. doi: 10.1016/j.apal.2024.103491

Author

Bagaviev, Ramil ; Batyrshin, Ilnur I. ; Bazhenov, Nikolay и др. / Computably and punctually universal spaces. в: Annals of Pure and Applied Logic. 2025 ; Том 176, № 1.

BibTeX

@article{72a16ca4aa3a4fd49c31efd344bad423,
title = "Computably and punctually universal spaces",
abstract = "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 Sierpi{\'n}ski in the 1940s. We prove that the original Urysohn's construction of the universal separable Polish space U is 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.",
keywords = "Computable Polish space, Continuous functions on the unit interval, Primitive recursive analysis, Punctual, Universal spaces",
author = "Ramil Bagaviev and Batyrshin, {Ilnur I.} and Nikolay Bazhenov and Dmitry Bushtets and Marina Dorzhieva and Koh, {Heer Tern} and Ruslan Kornev and Melnikov, {Alexander G.} and Ng, {Keng Meng}",
year = "2025",
month = jan,
doi = "10.1016/j.apal.2024.103491",
language = "English",
volume = "176",
journal = "Annals of Pure and Applied Logic",
issn = "0168-0072",
publisher = "Elsevier",
number = "1",

}

RIS

TY - JOUR

T1 - Computably and punctually universal spaces

AU - Bagaviev, Ramil

AU - Batyrshin, Ilnur I.

AU - Bazhenov, Nikolay

AU - Bushtets, Dmitry

AU - Dorzhieva, Marina

AU - Koh, Heer Tern

AU - Kornev, Ruslan

AU - Melnikov, Alexander G.

AU - Ng, Keng Meng

PY - 2025/1

Y1 - 2025/1

N2 - 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 U is 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.

AB - 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 U is 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.

KW - Computable Polish space

KW - Continuous functions on the unit interval

KW - Primitive recursive analysis

KW - Punctual

KW - Universal spaces

UR - https://www.mendeley.com/catalogue/201223d0-9465-375e-b32f-b1fcbc65209a/

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85200913507&origin=inward&txGid=91f4204e4737a9462e1b7b10407409d2

U2 - 10.1016/j.apal.2024.103491

DO - 10.1016/j.apal.2024.103491

M3 - Article

VL - 176

JO - Annals of Pure and Applied Logic

JF - Annals of Pure and Applied Logic

SN - 0168-0072

IS - 1

M1 - 103491

ER -

ID: 62768678