Open AccessWeak Darboux property and transitivity of linear mappings on topological vector spaces
Author(s) -
V. K. Maslyuchenko,
V. V. Nesterenko
Publication year - 2013
Publication title -
karpatsʹkì matematičnì publìkacìï
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.63
H-Index - 4
eISSN - 2313-0210
pISSN - 2075-9827
DOI - 10.15330/cmp.5.1.79-88
Subject(s) - mathematics , topological vector space , hausdorff space , transitive relation , topological space , vector space , pure mathematics , topology (electrical circuits) , normal space , discrete mathematics , combinatorics
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.