[[#cite_ref-Дьёдонне—1981—One_may_give_many_definitions_of_«Functional_Analysis»._Its_name_might_suggest_that_it_contains_all_parts_of_mathematics_which_deal_with_functions,_but_that_would_practically_mean_all_mathematical_Analysis._We_shall_adopt_a_narrower_definition:_for_us,_it_will_be_the_study_of_topological_vector_spaces_and_of_mappings_'"`UNIQ--math-0000001F-QINU`"'_from_a_part_'"`UNIQ--math-00000020-QINU`"'_of_a_topological_vector_space_'"`UNIQ--math-00000021-QINU`"'_into_a_topological_vector_space_'"`UNIQ--math-00000022-QINU`"',_these_mappings_being_assumed_to_satisfy_various_algebraic_and_topological_conditions—1_11-0|↑]] Дьёдонне, 1981, One may give many definitions of «Functional Analysis». Its name might suggest that it contains all parts of mathematics which deal with functions, but that would practically mean all mathematical Analysis. We shall adopt a narrower definition: for us, it will be the study of topological vector spaces and of mappings u : Ω → F {\displaystyle u:\Omega \to F} from a part Ω {\displaystyle \Omega } of a topological vector space E {\displaystyle E} into a topological vector space F {\displaystyle F} , these mappings being assumed to satisfy various algebraic and topological conditions, p. 1