Get quick answers to your questions about the article from our AI researcher chatbot
{'id': 'https://openalex.org/W2606251767', 'doi': 'https://doi.org/10.1515/9783110499469-013', 'title': 'B. Two elementary proofs of Brouwer’s fixed point theorem', 'display_name': 'B. Two elementary proofs of Brouwer’s fixed point theorem', 'publication_year': 2017, 'publication_date': '2017-04-10', 'ids': {'openalex': 'https://openalex.org/W2606251767', 'doi': 'https://doi.org/10.1515/9783110499469-013', 'mag': '2606251767'}, 'language': 'en', 'primary_location': {'is_oa': False, 'landing_page_url': 'https://doi.org/10.1515/9783110499469-013', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S4306463091', 'display_name': 'De Gruyter eBooks', 'issn_l': None, 'issn': None, 'is_oa': False, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/P4310313990', 'host_organization_name': 'De Gruyter', 'host_organization_lineage': ['https://openalex.org/P4310313990'], 'host_organization_lineage_names': ['De Gruyter'], 'type': 'ebook platform'}, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}, 'type': 'book-chapter', 'type_crossref': 'book-chapter', 'indexed_in': ['crossref'], 'open_access': {'is_oa': False, 'oa_status': 'closed', 'oa_url': None, 'any_repository_has_fulltext': False}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5034013841', 'display_name': 'Günter Mayer', 'orcid': None}, 'institutions': [], 'countries': [], 'is_corresponding': True, 'raw_author_name': 'Günter Mayer', 'raw_affiliation_strings': [], 'affiliations': []}], 'institution_assertions': [], 'countries_distinct_count': 0, 'institutions_distinct_count': 0, 'corresponding_author_ids': ['https://openalex.org/A5034013841'], 'corresponding_institution_ids': [], 'apc_list': None, 'apc_paid': None, 'fwci': 0.0, 'has_fulltext': True, 'fulltext_origin': 'ngrams', 'cited_by_count': 0, 'citation_normalized_percentile': {'value': 0.0, 'is_in_top_1_percent': False, 'is_in_top_10_percent': False}, 'cited_by_percentile_year': {'min': 0, 'max': 64}, 'biblio': {'volume': None, 'issue': None, 'first_page': '439', 'last_page': '444'}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T10792', 'display_name': 'Matrix Algorithms and Iterative Methods', 'score': 0.9109, 'subfield': {'id': 'https://openalex.org/subfields/1703', 'display_name': 'Computational Theory and Mathematics'}, 'field': {'id': 'https://openalex.org/fields/17', 'display_name': 'Computer Science'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}, 'topics': [{'id': 'https://openalex.org/T10792', 'display_name': 'Matrix Algorithms and Iterative Methods', 'score': 0.9109, 'subfield': {'id': 'https://openalex.org/subfields/1703', 'display_name': 'Computational Theory and Mathematics'}, 'field': {'id': 'https://openalex.org/fields/17', 'display_name': 'Computer Science'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}], 'keywords': [{'id': 'https://openalex.org/keywords/matrix-computations', 'display_name': 'Matrix Computations', 'score': 0.521269}, {'id': 'https://openalex.org/keywords/structured-preconditioners', 'display_name': 'Structured Preconditioners', 'score': 0.504472}, {'id': 'https://openalex.org/keywords/iterative-methods', 'display_name': 'Iterative Methods', 'score': 0.500822}], 'concepts': [{'id': 'https://openalex.org/C108710211', 'wikidata': 'https://www.wikidata.org/wiki/Q11538', 'display_name': 'Mathematical proof', 'level': 2, 'score': 0.7909627}, {'id': 'https://openalex.org/C45962547', 'wikidata': 'https://www.wikidata.org/wiki/Q1422068', 'display_name': 'Fixed-point theorem', 'level': 2, 'score': 0.63975585}, {'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.5827663}, {'id': 'https://openalex.org/C146147875', 'wikidata': 'https://www.wikidata.org/wiki/Q1144897', 'display_name': 'Brouwer fixed-point theorem', 'level': 3, 'score': 0.44400275}, {'id': 'https://openalex.org/C118615104', 'wikidata': 'https://www.wikidata.org/wiki/Q121416', 'display_name': 'Discrete mathematics', 'level': 1, 'score': 0.3960684}, {'id': 'https://openalex.org/C2524010', 'wikidata': 'https://www.wikidata.org/wiki/Q8087', 'display_name': 'Geometry', 'level': 1, 'score': 0.048117608}], 'mesh': [], 'locations_count': 1, 'locations': [{'is_oa': False, 'landing_page_url': 'https://doi.org/10.1515/9783110499469-013', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S4306463091', 'display_name': 'De Gruyter eBooks', 'issn_l': None, 'issn': None, 'is_oa': False, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/P4310313990', 'host_organization_name': 'De Gruyter', 'host_organization_lineage': ['https://openalex.org/P4310313990'], 'host_organization_lineage_names': ['De Gruyter'], 'type': 'ebook platform'}, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}], 'best_oa_location': None, 'sustainable_development_goals': [], 'grants': [], 'datasets': [], 'versions': [], 'referenced_works_count': 0, 'referenced_works': [], 'related_works': ['https://openalex.org/W4214541579', 'https://openalex.org/W3173188664', 'https://openalex.org/W3105975651', 'https://openalex.org/W2783180462', 'https://openalex.org/W2361904485', 'https://openalex.org/W2283967278', 'https://openalex.org/W2039551418', 'https://openalex.org/W2027036410', 'https://openalex.org/W2023675529', 'https://openalex.org/W2013342737'], 'abstract_inverted_index': None, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W2606251767', 'counts_by_year': [], 'updated_date': '2024-09-15T12:49:42.018026', 'created_date': '2017-04-28'}