On orthogonally additive injections and surjections (Q2822639)

Let \(V\) be a real inner product space and \(W\) a linear topological Hausdorff space.NEWLINENEWLINEUsing the ideas of \textit{K. Baron} [Ann. Univ. Sci. Budap. Rolando Eötvös, Sect. Comput. 40, 123--127 (2013; Zbl 1289.39049)], the author proves that if \(\mathrm{card}(V)\leq\mathrm{card}(W)\), then the set of all orthogonally additive injections mapping \(V\) into \(W\) is dense in the space of all orthogonally additive functions from \(V\) into \(W\) with the Tychonoff topology and that if \(\mathrm{card}(W)\leq\mathrm{card}(V)\), then the set of all orthogonally additive surjections mapping \(V\) into \(W\) is dense in the space of all orthogonally additive functions from \(V\) into \(W\) with the Tychonoff topology.NEWLINENEWLINEThe techniques and the ideas are simple and elementary and the paper is systematically well-organized.