{"@context":"https:\/\/schema.org\/","@type":"ScholarlyArticle","@id":"#article926","name":"The Construction of Finer Compact Topologies","abstract":"It is well known that each locally compact strongly sober topology is contained in a compact Hausdorff topology; just take the supremum of its topology with its dual topology. On the other hand, examples of compact topologies are known that do not have a finer compact Hausdorff topology.\r\nThis led to the question (first explicitly formulated by D.E. Cameron) whether each compact topology is contained in a compact topology with respect to which all compact sets are closed. (For the obvious reason these spaces are called maximal compact in the literature.)\r\nWhile this major problem remains open, we present several partial solutions to the question in our talk. For instance we show that each compact topology is contained in a compact topology with respect to which convergent sequences have unique limits. In fact each compact topology is contained in a compact topology with respect to which countable compact sets are closed. Furthermore we note that each compact sober T_1-topology is contained in a maximal compact topology and that each sober compact T_1-topology which is locally compact or sequential is the infimum of a family of maximal compact topologies.","keywords":["Maximal compact","KC-space","sober","US-space","locally compact","sequential","sequentially compact"],"author":[{"@type":"Person","name":"K\u00fcnzi, Hans-Peter A.","givenName":"Hans-Peter A.","familyName":"K\u00fcnzi"},{"@type":"Person","name":"Zypen, Dominic van der","givenName":"Dominic van der","familyName":"Zypen"}],"position":18,"pageStart":1,"pageEnd":5,"dateCreated":"2005-04-22","datePublished":"2005-04-22","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"K\u00fcnzi, Hans-Peter A.","givenName":"Hans-Peter A.","familyName":"K\u00fcnzi"},{"@type":"Person","name":"Zypen, Dominic van der","givenName":"Dominic van der","familyName":"Zypen"}],"copyrightYear":"2005","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.04351.18","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":{"@type":"PublicationVolume","@id":"#volume542","volumeNumber":4351,"name":"Dagstuhl Seminar Proceedings, Volume 4351","dateCreated":"2005-04-19","datePublished":"2005-04-19","isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#article926","isPartOf":{"@type":"Periodical","@id":"#series119","name":"Dagstuhl Seminar Proceedings","issn":"1862-4405","isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#volume542"}}}