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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\u0027s 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 (-\u221e, +\u221e) 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": "\u8457\u8005(\u30e8\u30df)", "attribute_value_mlt": [{"nameIdentifiers": [{"nameIdentifier": "69513", "nameIdentifierScheme": "WEKO"}], "names": [{"name": "\u30b5\u30ef\u30b7\u30de, \u30a4\u30af\u30b3"}]}]}, "item_11_publisher_36": {"attribute_name": "\u51fa\u7248\u8005", "attribute_value_mlt": [{"subitem_publisher": "\u304a\u8336\u306e\u6c34\u5973\u5b50\u5927\u5b66"}]}, "item_11_source_id_11": {"attribute_name": "\u66f8\u8a8c\u30ec\u30b3\u30fc\u30c9ID", "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": "\u65e5\u672c\u5341\u9032\u5206\u985e\u6cd5", "attribute_value_mlt": [{"subitem_subject": "400", "subitem_subject_scheme": "NDC"}]}, "item_11_text_18": {"attribute_name": "\u5f62\u614b", "attribute_value_mlt": [{"subitem_text_value": "611032 bytes"}]}, "item_11_text_47": {"attribute_name": "\u8cc7\u6e90\u30bf\u30a4\u30d7\u30fb\u30ed\u30fc\u30ab\u30eb", "attribute_value_mlt": [{"subitem_text_value": "\u7d00\u8981\u8ad6\u6587"}]}, "item_11_text_48": {"attribute_name": "\u8cc7\u6e90\u30bf\u30a4\u30d7\u30fbNII", "attribute_value_mlt": [{"subitem_text_value": "Departmental Bulletin Paper"}]}, "item_11_text_49": {"attribute_name": "\u8cc7\u6e90\u30bf\u30a4\u30d7\u30fbDCMI", "attribute_value_mlt": [{"subitem_text_value": "text"}]}, "item_11_text_50": {"attribute_name": "\u8cc7\u6e90\u30bf\u30a4\u30d7\u30fb\u30ed\u30fc\u30ab\u30eb\u8868\u793a\u30b3\u30fc\u30c9", "attribute_value_mlt": [{"subitem_text_value": "03"}]}, "item_11_text_79": {"attribute_name": "\u6240\u5c5e", "attribute_value_mlt": [{"subitem_text_value": "Department of Mathematics, Faculty of Science, Ochanomizu University"}]}, "item_creator": {"attribute_name": "\u8457\u8005", "attribute_type": "creator", "attribute_value_mlt": [{"creatorNames": [{"creatorName": "Sawashima, Ikuko"}], "nameIdentifiers": [{"nameIdentifier": "69512", "nameIdentifierScheme": "WEKO"}]}, {"creatorNames": [{"creatorName": "\u6ca2\u5cf6, \u4f91\u5b50", "creatorNameLang": "en"}], "nameIdentifiers": [{"nameIdentifier": "69514", "nameIdentifierScheme": "WEKO"}]}]}, "item_files": {"attribute_name": "\u30d5\u30a1\u30a4\u30eb\u60c5\u5831", "attribute_type": "file", "attribute_value_mlt": [{"accessrole": "open_date", "date": [{"dateType": "Available", "dateValue": "2018-04-19"}], "displaytype": "detail", "download_preview_message": "", "file_order": 0, "filename": "KJ00004829511.pdf", "filesize": [{"value": "611.0 kB"}], "format": "application/pdf", "future_date_message": "", "is_thumbnail": false, "licensetype": "license_free", "mimetype": "application/pdf", "size": 611000.0, "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": "\u8a00\u8a9e", "attribute_value_mlt": [{"subitem_language": "eng"}]}, "item_resource_type": {"attribute_name": "\u8cc7\u6e90\u30bf\u30a4\u30d7", "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": "\u30bf\u30a4\u30c8\u30eb", "attribute_value_mlt": [{"subitem_title": "Locally Convex Spaces with the Extension Property"}]}, "item_type_id": "11", "owner": "1", "path": ["347/359/594"], "permalink_uri": "http://hdl.handle.net/10083/2082", "pubdate": {"attribute_name": "\u516c\u958b\u65e5", "attribute_name_i18n": "\u516c\u958b\u65e5", "attribute_value": "2008-04-30"}, "publish_date": "2008-04-30", "publish_status": "0", "recid": "35005", "relation": {}, "relation_version_is_last": true, "title": ["Locally Convex Spaces with the Extension Property"], "weko_shared_id": null}