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

Authors

  • V.K. Maslyuchenko Yuriy Fedkovych Chernivtsi National University, 2 Kotsjubynskyi str., 58012, Chernivtsi, Ukraine
  • V.V. Nesterenko Yuriy Fedkovych Chernivtsi National University, 2 Kotsjubynskyi str., 58012, Chernivtsi, Ukraine
https://doi.org/10.15330/cmp.5.1.79-88

Keywords:

linear mapping, Darboux property, transitive mapping, closed graph, closed kernel
Published online: 2013-06-20

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.

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How to Cite
(1)
Maslyuchenko, V.; Nesterenko, V. Weak Darboux Property and Transitivity of Linear Mappings on Topological Vector Spaces. Carpathian Math. Publ. 2013, 5, 79-88.