{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/72793"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/72793","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"On the topology of the spaces of coverings","abstract":"The spaces of coverings (SoC) arise from various configuration spaces of the covering problems. We study the topology of these spaces for different domains and covering agents. In particular, we study the SoCs for grid domains and metric trees covered by balls. Characterizations of their topology are given for analysis of the topological complexities (the Betti numbers in all dimensions). We also study the spaces of fort coverings, a topological approximation of the SoCs capturing some essential features of the SoCs. The applications of the SoCs abound, in the end we present the feedback control on the SoC for metric tree coverage as a case study.","abstract_html":"The spaces of coverings (SoC) arise from various configuration spaces of the covering problems. We study the topology of these spaces for different domains and covering agents. In particular, we study the SoCs for grid domains and metric trees covered by balls. Characterizations of their topology are given for analysis of the topological complexities (the Betti numbers in all dimensions). We also study the spaces of fort coverings, a topological approximation of the SoCs capturing some essential features of the SoCs. The applications of the SoCs abound, in the end we present the feedback control on the SoC for metric tree coverage as a case study.","abstract_has_math":false,"creators":["Wang, Han"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Baryshnikov, Yuliy","Schenck, Hal","Hirani, Anil","Zharnitsky, Vadim"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-01-21T19:48:15Z","date_published":"2015-01-21T19:48:15Z","updated_at":"2026-07-22T22:26:07Z","subjects":["Covering","Topology","Configuration space","Feedback Control"],"languages":["en"],"rights":["Copyright 2014 Han Wang"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/72793","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Baryshnikov, Yuliy","Schenck, Hal","Hirani, Anil","Zharnitsky, Vadim"]},{"key":"dc:creator","label":"Author","values":["Wang, Han"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2015-01-21T19:48:15Z","2014-12","2015-01-21"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Covering","Topology","Configuration space","Feedback Control"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2014 Han Wang"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/72793"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["The spaces of coverings (SoC) arise from various configuration spaces of the covering problems. We study the topology of these spaces for different domains and covering agents. In particular, we study the SoCs for grid domains and metric trees covered by balls. Characterizations of their topology are given for analysis of the topological complexities (the Betti numbers in all dimensions). We also study the spaces of fort coverings, a topological approximation of the SoCs capturing some essential features of the SoCs. The applications of the SoCs abound, in the end we present the feedback control on the SoC for metric tree coverage as a case study.","Item withdrawn by Laura Spradlin (lspradl2@illinois.edu) on 2014-12-04T20:23:29Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 Wang_Han.pdf: 20911608 bytes, checksum: 8b1d6939749948747120b634f473fdab (MD5)","Made available in DSpace on 2015-01-21T19:48:15Z (GMT). No. of bitstreams: 1 Han_Wang.pdf: 20911608 bytes, checksum: 8b1d6939749948747120b634f473fdab (MD5)"]},{"key":"dc:title","label":"Title","values":["On the topology of the spaces of coverings"]}]}],"canonical_facts":{"dc:contributor":["Baryshnikov, Yuliy","Schenck, Hal","Hirani, Anil","Zharnitsky, Vadim"],"dc:creator":["Wang, Han"],"dc:date":["2015-01-21T19:48:15Z","2014-12","2015-01-21"],"dc:description":["The spaces of coverings (SoC) arise from various configuration spaces of the covering problems. We study the topology of these spaces for different domains and covering agents. In particular, we study the SoCs for grid domains and metric trees covered by balls. Characterizations of their topology are given for analysis of the topological complexities (the Betti numbers in all dimensions). We also study the spaces of fort coverings, a topological approximation of the SoCs capturing some essential features of the SoCs. The applications of the SoCs abound, in the end we present the feedback control on the SoC for metric tree coverage as a case study.","Item withdrawn by Laura Spradlin (lspradl2@illinois.edu) on 2014-12-04T20:23:29Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 Wang_Han.pdf: 20911608 bytes, checksum: 8b1d6939749948747120b634f473fdab (MD5)","Made available in DSpace on 2015-01-21T19:48:15Z (GMT). No. of bitstreams: 1 Han_Wang.pdf: 20911608 bytes, checksum: 8b1d6939749948747120b634f473fdab (MD5)"],"dc:identifier":["http://hdl.handle.net/2142/72793"],"dc:language":["en"],"dc:rights":["Copyright 2014 Han Wang"],"dc:subject":["Covering","Topology","Configuration space","Feedback Control"],"dc:title":["On the topology of the spaces of coverings"],"dc:type":["text"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:26:07Z"}