{"created":"2021-03-01T06:40:21.990586+00:00","id":35005,"links":{},"metadata":{"_buckets":{"deposit":"68c4f7ba-a38a-4e91-821d-1bf835a5d514"},"_deposit":{"id":"35005","owners":[],"pid":{"revision_id":0,"type":"depid","value":"35005"},"status":"published"},"_oai":{"id":"oai:teapot.lib.ocha.ac.jp:00035005","sets":["347:359:594"]},"item_11_biblio_info_8":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"1960-07","bibliographicIssueDateType":"Issued"},"bibliographicIssueNumber":"1","bibliographicPageEnd":"27","bibliographicPageStart":"19","bibliographicVolumeNumber":"11","bibliographic_titles":[{"bibliographic_title":"お茶の水女子大學自然科學報告"}]}]},"item_11_description_17":{"attribute_name":"フォーマット","attribute_value_mlt":[{"subitem_description":"application/pdf","subitem_description_type":"Other"}]},"item_11_description_46":{"attribute_name":"資源タイプ","attribute_value_mlt":[{"subitem_description":"紀要論文","subitem_description_type":"Other"}]},"item_11_description_7":{"attribute_name":"内容記述","attribute_value_mlt":[{"subitem_description":"There are several researches on a normed space N with the extension property : each continuous linear function f on a subspace of any normed space with values in N has a linear extension f' on the whole space such that ‖f‖=‖f'‖. Among those, the following result has been obtained by L. Nachbin [4] ; a normed space has the extension property if and only if the collection of all its spheres has the binary intersection property. The collection U of all spheres is said to have the binary intersection property if every subcollection of U, any two elements of which intersect, has a nonvoid intersection. In this paper, we shall give a convenient definition of extension property of locally convex topological vector spaces. Of course the property must be a generalization of the usual extension property. Theorem 1 gives a necessary and sufficient condition in order that a locally convex space should have the extension property in our sense which corresponds with Nachbin's result. Theorem 2 gives a characterization of a locally convex topological vector space having the extension property. A vector space E is said to be a\\\ntopological vector space if E is a Hausdorff space in which the vector operations, summation and scalar multiplication, are continuous for the topology. Moreover, if the neighbourhood system in a topological vector space consists of convex sets, then E is said to be a locally convex topological vector space or a locally convex space. In this paper, the neighbourhood system in a locally convex space is always assumed, without loss of generality, to consist of symmetric, convex closed sets. We shall denote by R the real space (-∞, +∞) and {x ; P(x)} the set of all the elements with the property P(x).","subitem_description_type":"Other"}]},"item_11_full_name_2":{"attribute_name":"著者(ヨミ)","attribute_value_mlt":[{"nameIdentifiers":[{"nameIdentifier":"69513","nameIdentifierScheme":"WEKO"}],"names":[{"name":"サワシマ, イクコ"}]}]},"item_11_publisher_36":{"attribute_name":"出版者","attribute_value_mlt":[{"subitem_publisher":"お茶の水女子大学"}]},"item_11_source_id_11":{"attribute_name":"書誌レコードID","attribute_value_mlt":[{"subitem_source_identifier":"AN00033958","subitem_source_identifier_type":"NCID"}]},"item_11_source_id_9":{"attribute_name":"ISSN","attribute_value_mlt":[{"subitem_source_identifier":"00298190","subitem_source_identifier_type":"ISSN"}]},"item_11_subject_20":{"attribute_name":"日本十進分類法","attribute_value_mlt":[{"subitem_subject":"400","subitem_subject_scheme":"NDC"}]},"item_11_text_18":{"attribute_name":"形態","attribute_value_mlt":[{"subitem_text_value":"611032 bytes"}]},"item_11_text_47":{"attribute_name":"資源タイプ・ローカル","attribute_value_mlt":[{"subitem_text_value":"紀要論文"}]},"item_11_text_48":{"attribute_name":"資源タイプ・NII","attribute_value_mlt":[{"subitem_text_value":"Departmental Bulletin Paper"}]},"item_11_text_49":{"attribute_name":"資源タイプ・DCMI","attribute_value_mlt":[{"subitem_text_value":"text"}]},"item_11_text_50":{"attribute_name":"資源タイプ・ローカル表示コード","attribute_value_mlt":[{"subitem_text_value":"03"}]},"item_11_text_79":{"attribute_name":"所属","attribute_value_mlt":[{"subitem_text_value":"Department of Mathematics, Faculty of Science, Ochanomizu University"}]},"item_creator":{"attribute_name":"著者","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"Sawashima, Ikuko"}],"nameIdentifiers":[{"nameIdentifier":"69512","nameIdentifierScheme":"WEKO"}]},{"creatorNames":[{"creatorName":"沢島, 侑子","creatorNameLang":"en"}],"nameIdentifiers":[{"nameIdentifier":"69514","nameIdentifierScheme":"WEKO"}]}]},"item_files":{"attribute_name":"ファイル情報","attribute_type":"file","attribute_value_mlt":[{"accessrole":"open_date","date":[{"dateType":"Available","dateValue":"2018-04-19"}],"displaytype":"detail","filename":"KJ00004829511.pdf","filesize":[{"value":"611.0 kB"}],"format":"application/pdf","licensetype":"license_note","mimetype":"application/pdf","url":{"label":"KJ00004829511.pdf","url":"https://teapot.lib.ocha.ac.jp/record/35005/files/KJ00004829511.pdf"},"version_id":"53600770-961d-4a30-9dbb-8e5d91da6696"}]},"item_language":{"attribute_name":"言語","attribute_value_mlt":[{"subitem_language":"eng"}]},"item_resource_type":{"attribute_name":"資源タイプ","attribute_value_mlt":[{"resourcetype":"departmental bulletin paper","resourceuri":"http://purl.org/coar/resource_type/c_6501"}]},"item_title":"Locally Convex Spaces with the Extension Property","item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"Locally Convex Spaces with the Extension Property"}]},"item_type_id":"11","owner":"1","path":["594"],"pubdate":{"attribute_name":"公開日","attribute_value":"2008-04-30"},"publish_date":"2008-04-30","publish_status":"0","recid":"35005","relation_version_is_last":true,"title":["Locally Convex Spaces with the Extension Property"],"weko_creator_id":"1","weko_shared_id":null},"updated":"2022-12-12T05:39:56.689348+00:00"}