|
In functional analysis and related areas of mathematics the strong topology is the finest polar topology, the topology with the most open sets, on a dual pair. The coarsest polar topology is called weak topology. == Definition == Let be a dual pair of vector spaces over the field of real () or complex () numbers. Let us denote by the system of all subsets bounded by elements of in the following sense: : Then the strong topology on is defined as the locally convex topology on generated by the seminorms of the form : In the special case when is a locally convex space, the strong topology on the (continuous) dual space (i.e. on the space of all continuous linear functionals ) is defined as the strong topology , and it coincides with the topology of uniform convergence on bounded sets in , i.e. with the topology on generated by the seminorms of the form : where runs over the family of all bounded sets in . The space with this topology is called strong dual space of the space and is denoted by . 抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)』 ■ウィキペディアで「Strong topology (polar topology)」の詳細全文を読む スポンサード リンク
|