{"title":"利用分段不相交弧盘性质及相关性质检测余维数","authors":"D. Halverson, Dušan D. Repovš","doi":"10.2478/s11533-013-0291-z","DOIUrl":null,"url":null,"abstract":"We show that all finite-dimensional resolvable generalized manifolds with the piecewise disjoint arc-disk property are codimension one manifold factors. We then show how the piecewise disjoint arc-disk property and other general position properties that detect codimension one manifold factors are related. We also note that in every example presently known to the authors of a codimension one manifold factor of dimension n ≥ 4 determined by general position properties, the piecewise disjoint arc-disk property is satisfied.","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"67 1","pages":"1932-1948"},"PeriodicalIF":0.0000,"publicationDate":"2013-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Detecting codimension one manifold factors with the piecewise disjoint arc-disk property and related properties\",\"authors\":\"D. Halverson, Dušan D. Repovš\",\"doi\":\"10.2478/s11533-013-0291-z\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We show that all finite-dimensional resolvable generalized manifolds with the piecewise disjoint arc-disk property are codimension one manifold factors. We then show how the piecewise disjoint arc-disk property and other general position properties that detect codimension one manifold factors are related. We also note that in every example presently known to the authors of a codimension one manifold factor of dimension n ≥ 4 determined by general position properties, the piecewise disjoint arc-disk property is satisfied.\",\"PeriodicalId\":50988,\"journal\":{\"name\":\"Central European Journal of Mathematics\",\"volume\":\"67 1\",\"pages\":\"1932-1948\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2013-08-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Central European Journal of Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2478/s11533-013-0291-z\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Central European Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2478/s11533-013-0291-z","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Detecting codimension one manifold factors with the piecewise disjoint arc-disk property and related properties
We show that all finite-dimensional resolvable generalized manifolds with the piecewise disjoint arc-disk property are codimension one manifold factors. We then show how the piecewise disjoint arc-disk property and other general position properties that detect codimension one manifold factors are related. We also note that in every example presently known to the authors of a codimension one manifold factor of dimension n ≥ 4 determined by general position properties, the piecewise disjoint arc-disk property is satisfied.