Cattaneo, G.; Marino, G. Some interesting posets of subspace of a pre-Hilbert space. (Italian. English summary) Zbl 0599.46023 Rend. Sem. Mat. Fis. Milano 53, 69-74 (1983). We introduce and study three remarkable families of subspaces in a pre- Hilbert space from the ordering point of view. The completeness of the pre-Hilbert space is characterized by means of the properties which the three families have with respect to the ordering. Cited in 1 Document MSC: 46C99 Inner product spaces and their generalizations, Hilbert spaces Keywords:families of subspaces in a pre-Hilbert space; completeness PDFBibTeX XMLCite \textit{G. Cattaneo} and \textit{G. Marino}, Rend. Semin. Mat. Fis. Milano 53, 69--74 (1983; Zbl 0599.46023) Full Text: DOI References: [1] Amemiya I., Araki H.,A remark on Piron’s paper. Publ. Res. Inst. Math. Sci. Ser. A, 12 (1966), 423–427. · Zbl 0177.16103 [2] Cattaneo G., Franco G.,Ordering properties of subspaces, exact subspaces and orthospaces in pre-Hilbert spaces: the logics of pre-Hilbert spaces. Preprint DMUC/Oct (1983). [3] Cattaneo G., Marino G.,Completeness characterization of an inner product space with respect to splitting subspaces. Preprint DMUC/Dec. (1985). · Zbl 0601.46026 [4] Gudder S. P.,Inner product spaces. Am. Math. Monhtly 81 (1974), 29–36. · Zbl 0279.46013 [5] Gudder S. P.,Correction to “Inner product spaces{”. Am. Math. Monthly 82 (1975), 251–252.} · Zbl 0305.46033 [6] Gudder S. P., Holland S.,Second correction to “Inner product spaces{”. Am. Math. Monthly 82 (1975), 818.} · Zbl 0305.46033 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.