{"title":"Compactification of Spaces of Measures and Pseudocompactness","authors":"V. I. Bogachev","doi":"10.1134/S1064562424702181","DOIUrl":null,"url":null,"abstract":"<p>We prove pseudocompactness of a Tychonoff space <i>X</i> and the space <span>\\(\\mathcal{P}(X)\\)</span> of Radon probability measures on it with the weak topology under the condition that the Stone–Čech compactification of the space <span>\\(\\mathcal{P}(X)\\)</span> is homeomorphic to the space <span>\\(\\mathcal{P}(\\beta X)\\)</span> of Radon probability measures on the Stone–Čech compactification of the space <i>X</i>.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"110 1","pages":"357 - 360"},"PeriodicalIF":0.5000,"publicationDate":"2024-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Doklady Mathematics","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1134/S1064562424702181","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We prove pseudocompactness of a Tychonoff space X and the space \(\mathcal{P}(X)\) of Radon probability measures on it with the weak topology under the condition that the Stone–Čech compactification of the space \(\mathcal{P}(X)\) is homeomorphic to the space \(\mathcal{P}(\beta X)\) of Radon probability measures on the Stone–Čech compactification of the space X.
期刊介绍：
Doklady Mathematics is a journal of the Presidium of the Russian Academy of Sciences. It contains English translations of papers published in Doklady Akademii Nauk (Proceedings of the Russian Academy of Sciences), which was founded in 1933 and is published 36 times a year. Doklady Mathematics includes the materials from the following areas: mathematics, mathematical physics, computer science, control theory, and computers. It publishes brief scientific reports on previously unpublished significant new research in mathematics and its applications. The main contributors to the journal are Members of the RAS, Corresponding Members of the RAS, and scientists from the former Soviet Union and other foreign countries. Among the contributors are the outstanding Russian mathematicians.
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