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

DOI:

https://doi.org/10.15330/cmp.5.1.79-88

Keywords:

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

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.

Additional Files

Published

2013-06-20

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.

Issue

Section

Scientific articles