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

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 with values in Hausdorff topological vector space the following conditions are equivalent: (i) is continuous; (ii) graph of is closed; (iii) kernel of is closed; (iv) is transition map.
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.