Weak Darboux property and transitivity of linear mappings on topological vector spaces

V. K. Maslyuchenko, V. V. Nesterenko

Abstract


It is shown that every linear mapping on topological vector spaces always has weak Darboux property, therefore, it is continuous if and only if it is transitive. For finite-dimensional mapping $f$ with values in Hausdorff topological vector space the following conditions are equivalent: (i) $f$ is continuous; (ii) graph of $f$ is closed; (iii) kernel of $f$ is closed; (iv) $f$ is transition map.

Keywords


Linear mapping, Darboux property, transitive mapping, closed graph, closed kernel

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