{"title":"紧类中绝对伸展量与单元的乘法几何","authors":"M. Zarichnyǐ","doi":"10.1070/SM1993V074N01ABEH003331","DOIUrl":null,"url":null,"abstract":"An investigation is made of the geometry of the multiplication mappings for monads whose functorial parts are (weakly) normal (in the sense of Shchepin) functors acting in the category of compacta. A characterization is obtained for a power monad as the only normal monad such that the multiplication mapping is soft for some \\omega_1$ SRC=http://ej.iop.org/images/0025-5734/74/1/A02/tex_sm_3331_img4.gif/>. It is proved that the multiplication mappings and of the inclusion hyperspace monad and the monad of complete chained systems are homeomorphic to trivial Tychonoff fibrations for openly generated continua that are homogeneous with respect to character.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"10 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1993-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"ABSOLUTE EXTENSORS AND THE GEOMETRY OF MULTIPLICATION OF MONADS IN THE CATEGORY OF COMPACTA\",\"authors\":\"M. Zarichnyǐ\",\"doi\":\"10.1070/SM1993V074N01ABEH003331\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"An investigation is made of the geometry of the multiplication mappings for monads whose functorial parts are (weakly) normal (in the sense of Shchepin) functors acting in the category of compacta. A characterization is obtained for a power monad as the only normal monad such that the multiplication mapping is soft for some \\\\omega_1$ SRC=http://ej.iop.org/images/0025-5734/74/1/A02/tex_sm_3331_img4.gif/>. It is proved that the multiplication mappings and of the inclusion hyperspace monad and the monad of complete chained systems are homeomorphic to trivial Tychonoff fibrations for openly generated continua that are homogeneous with respect to character.\",\"PeriodicalId\":208776,\"journal\":{\"name\":\"Mathematics of The Ussr-sbornik\",\"volume\":\"10 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1993-02-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematics of The Ussr-sbornik\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1070/SM1993V074N01ABEH003331\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematics of The Ussr-sbornik","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1070/SM1993V074N01ABEH003331","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
ABSOLUTE EXTENSORS AND THE GEOMETRY OF MULTIPLICATION OF MONADS IN THE CATEGORY OF COMPACTA
An investigation is made of the geometry of the multiplication mappings for monads whose functorial parts are (weakly) normal (in the sense of Shchepin) functors acting in the category of compacta. A characterization is obtained for a power monad as the only normal monad such that the multiplication mapping is soft for some \omega_1$ SRC=http://ej.iop.org/images/0025-5734/74/1/A02/tex_sm_3331_img4.gif/>. It is proved that the multiplication mappings and of the inclusion hyperspace monad and the monad of complete chained systems are homeomorphic to trivial Tychonoff fibrations for openly generated continua that are homogeneous with respect to character.
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