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On orthogonal projections of Nöbeling spaces

Suppose that . We prove that there is a dense open subset of the Grassmann space such that the orthogonal projection of the standard Nöbeling space (which lies in for sufficiently large ) to every -dimensional plane in this subset is -soft and possesses the strong -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.