On orthogonally additive functions with big graphs
Abstract
Let E be a separable real inner product space of dimension at least 2 and V be a metrizable and separable linear topological space. We show that the set of all orthogonally additive functions mapping E into V and having big graphs is dense in the space of all orthogonally additive functions from E into V with the Tychonoff topology.
Keywords
orthogonal additivity; inner product space; linear topological space; Tychonoff topology; big graph; dense set
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Instytut Matematyki, Uniwersytet Śląski w Katowicach Poland
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