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

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 c...

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Main Authors:	V.K. Maslyuchenko, V.V. Nesterenko
Format:	Article
Language:	English
Published:	Vasyl Stefanyk Precarpathian National University 2013-06-01
Series:	Karpatsʹkì Matematičnì Publìkacìï
Subjects:	linear mapping darboux property transitive mapping closed graph closed kernel
Online Access:	https://journals.pnu.edu.ua/index.php/cmp/article/view/3654

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spelling	doaj-28a625deda2044179abd6008843d0da72020-11-25T03:38:22ZengVasyl Stefanyk Precarpathian National UniversityKarpatsʹkì Matematičnì Publìkacìï2075-98272313-02102013-06-0151798810.15330/cmp.5.1.79-883654Weak Darboux property and transitivity of linear mappings on topological vector spacesV.K. Maslyuchenko0V.V. Nesterenko1Yuriy Fedkovych Chernivtsi National University, 2 Kotsjubynskyi str., 58012, Chernivtsi, UkraineYuriy Fedkovych Chernivtsi National University, 2 Kotsjubynskyi str., 58012, Chernivtsi, UkraineIt 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.https://journals.pnu.edu.ua/index.php/cmp/article/view/3654linear mappingdarboux propertytransitive mappingclosed graphclosed kernel
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	V.K. Maslyuchenko V.V. Nesterenko
spellingShingle	V.K. Maslyuchenko V.V. Nesterenko Weak Darboux property and transitivity of linear mappings on topological vector spaces Karpatsʹkì Matematičnì Publìkacìï linear mapping darboux property transitive mapping closed graph closed kernel
author_facet	V.K. Maslyuchenko V.V. Nesterenko
author_sort	V.K. Maslyuchenko
title	Weak Darboux property and transitivity of linear mappings on topological vector spaces
title_short	Weak Darboux property and transitivity of linear mappings on topological vector spaces
title_full	Weak Darboux property and transitivity of linear mappings on topological vector spaces
title_fullStr	Weak Darboux property and transitivity of linear mappings on topological vector spaces
title_full_unstemmed	Weak Darboux property and transitivity of linear mappings on topological vector spaces
title_sort	weak darboux property and transitivity of linear mappings on topological vector spaces
publisher	Vasyl Stefanyk Precarpathian National University
series	Karpatsʹkì Matematičnì Publìkacìï
issn	2075-9827 2313-0210
publishDate	2013-06-01
description	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.
topic	linear mapping darboux property transitive mapping closed graph closed kernel
url	https://journals.pnu.edu.ua/index.php/cmp/article/view/3654
work_keys_str_mv	AT vkmaslyuchenko weakdarbouxpropertyandtransitivityoflinearmappingsontopologicalvectorspaces AT vvnesterenko weakdarbouxpropertyandtransitivityoflinearmappingsontopologicalvectorspaces
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Weak Darboux property and transitivity of linear mappings on topological vector spaces

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