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Izv. RAN. Ser. Mat., 2020, Volume 84, Issue 4, Pages 5–40 (Mi izv8910)  

On orthogonal projections of Nöbeling spaces

S. M. Ageev

Belarusian State University

Abstract: Suppose that $0\le k<\infty$. We prove that there is a dense open subset of the Grassmann space $\operatorname{Gr}(2k+1,m)$ such that the orthogonal projection of the standard Nöbeling space $N^m_k$ (which lies in $\mathbb R^m$ for sufficiently large $m$) to every $(2k+1)$-dimensional plane in this subset is $k$-soft and possesses the strong $k$-universal property with respect to Polish spaces. Every such orthogonal projection is a natural counterpart of the standard Nöbeling space for the category of maps.

Keywords: Nöbeling space, Dranishnikov and Chigogidze resolutions, strong fibrewise $k$-universal property, filtered finite-dimensional selection theorem, $\operatorname{AE}(k)$-space.

Funding Agency Grant Number
Ministry of Education of the Republic of Belarus
This paper was written with the partial support of a~grant from the Ministry of~Education of~the Belarusian Republic.


DOI: https://doi.org/10.4213/im8910

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English version:
Izvestiya: Mathematics, 2020, 84:4, 627–658

Bibliographic databases:

UDC: 515.126.83+515.124.62
MSC: 54F65, 57N20, 54C53, 55P15
Received: 02.03.2019
Revised: 01.07.2019

Citation: S. M. Ageev, “On orthogonal projections of Nöbeling spaces”, Izv. RAN. Ser. Mat., 84:4 (2020), 5–40; Izv. Math., 84:4 (2020), 627–658

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