naa a22 4500 510782868 CHVBK 20180411083253.0 cr unu---uuuuu 180411e20130601xx s 000 0 eng 10.1007/s11856-012-0113-1 doi (NATIONALLICENCE)springer-10.1007/s11856-012-0113-1 Classifying Erdős type spaces of higher descriptive complexity [Elektronische Daten] [Jan Dijkstra, Kirsten Valkenburg] Let $${({E_n})_{n \in \omega }}$$ be a sequence of zero-dimensional subsets of the reals, ℝ. The Erdős type space ɛ corresponding to this sequence is defined by ɛ = {x ∈ ℓ 2: x n ∈ E n , n ∈ω}. The most famous examples are Erdős space, with E n equal to the rationals for each n, and complete Erdős space, with E n = {0} ∪ {1/m: m ∈ ℕ} for each n. If all sets E n are $${G_\delta }$$ and the space ɛ is not zero-dimensional, then ɛ is known to be homeomorphic to complete Erdős space, and if all sets E n are $${F_{\sigma \delta }}$$ , then under a mild additional condition ɛ is known to be homeomorphic to Erdős space. In this paper we investigate the situation where all sets E n are Borel sets in the same multiplicative class. Many of these spaces can be linked to the Erdős type space with all sets E n equal to the element of that multiplicative Borel class which absorbs the class. Furthermore, we introduce coanalytic Erdős space and we establish a link between this space and homeomorphism groups of manifolds that leave the zero-dimensional pseudoboundary invariant. The general framework that we develop gives analogous results for nonseparable Erdős type spaces. Hebrew University Magnes Press, 2013 Dijkstra Jan Faculteit der Exacte Wetenschappen/Afdeling Wiskunde, Vrije Universiteit, De Boelelaan 1081a, 1081 HV, Amsterdam, The Netherlands aut Valkenburg Kirsten Department of Mathematics and Statistics, University of Saskatchewan, 106 Wiggins Road, S7N 5E6, Saskatoon, SK, Canada aut Israel Journal of Mathematics Springer US; http://www.springer-ny.com 195/2(2013-06-01), 725-744 0021-2172 195:2<725 2013 195 11856 https://doi.org/10.1007/s11856-012-0113-1 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11856-012-0113-1 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Dijkstra Jan Faculteit der Exacte Wetenschappen/Afdeling Wiskunde, Vrije Universiteit, De Boelelaan 1081a, 1081 HV, Amsterdam, The Netherlands aut NATIONALLICENCE 700 1- Valkenburg Kirsten Department of Mathematics and Statistics, University of Saskatchewan, 106 Wiggins Road, S7N 5E6, Saskatoon, SK, Canada aut NATIONALLICENCE 773 0- Israel Journal of Mathematics Springer US; http://www.springer-ny.com 195/2(2013-06-01), 725-744 0021-2172 195:2<725 2013 195 11856 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer