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

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Author(s): V. K. Maslyuchenko | V. V. Nesterenko

Journal: Carpathian Mathematical Publications
ISSN 2075-9827

Volume: 5;
Issue: 1;
Start page: 79;
Date: 2013;
Original page

Keywords: Linear mapping | Darboux property | transitive mapping | closed graph | closed kernel

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