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On orthogonal projections of Nöbeling spaces
S. M. Ageev Belarusian State University
Abstract:
Suppose that 0⩽k<∞. We prove that there is a dense open subset of the Grassmann space
Gr(2k+1,m) such that the orthogonal projection of the standard Nöbeling space
Nmk (which lies in Rm 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, AE(k)-space.
Received: 02.03.2019 Revised: 01.07.2019
Citation:
S. M. Ageev, “On orthogonal projections of Nöbeling spaces”, Izv. Math., 84:4 (2020), 627–658
Linking options:
https://www.mathnet.ru/eng/im8910https://doi.org/10.1070/IM8910 https://www.mathnet.ru/eng/im/v84/i4/p5
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Abstract page: | 385 | Russian version PDF: | 56 | English version PDF: | 34 | References: | 67 | First page: | 15 |
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