Ageev, S. M.; Bogatyj, S. A.; Repovš, D. The complement \(Q_ E(n)\) of the point \(\mathrm{Eucl}\) of the Euclidean space in the Banach-Mazur compactum \(Q(n)\) is a \(Q\)-manifold. (English. Russian original) Zbl 1054.57026 Russ. Math. Surv. 58, No. 3, 607-609 (2003); translation from Usp. Mat. Nauk 58, No. 3, 185-186 (2003). Let \(Q(n)\) denote the Banach-Mazur compactum, that is the space of isometry classes of \(n\)-dimensional Banach-spaces. Let \(\{\text{Eucl} \}\in Q(n)\) denote the Euclidean point to which corresponds the isometry class of standard \(n\)-dimensional Euclidean space. The authors show, Theorem 2, \(Q_E(n)=Q(n)\setminus \{\text{Eucl}\}\) is a \(Q\)-manifold (where \(Q\) denotes the Hilbert cube). Cited in 1 Review MSC: 57N20 Topology of infinite-dimensional manifolds 46B99 Normed linear spaces and Banach spaces; Banach lattices 54C55 Absolute neighborhood extensor, absolute extensor, absolute neighborhood retract (ANR), absolute retract spaces (general properties) Keywords:Hilbert cube manifold PDFBibTeX XMLCite \textit{S. M. Ageev} et al., Russ. Math. Surv. 58, No. 3, 607--609 (2003; Zbl 1054.57026); translation from Usp. Mat. Nauk 58, No. 3, 185--186 (2003) Full Text: DOI