幂等概率测度空间的几何性质

IF 0.6 Q3 MATHEMATICS

Applied general topology Pub Date : 2021-10-01 DOI:10.4995/agt.2021.15101

Kholsaid Kholturayev

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引用次数: 5

摘要

虽然传统数学和幂等数学是“平行的”，但通过范畴论的应用，我们证明了在传统数学和幂等数学上得到相似规则的对象不一定是“平行的”。首先，我们建立了紧度量空间X的概率测度空间P(X)和幂等概率测度空间I(X)是同胚的(“平行性”)。然后，我们构造了一个例子，表明结构P和I形成了彼此不同的函子(“并行”否定)。进一步地，对于紧Hausdorff空间X，我们证明了I3(X)\ X的遗传正规性暗示了X的度量性。

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Geometrical properties of the space of idempotent probability measures

Although traditional and idempotent mathematics are "parallel'', by an application of the category theory we show that objects obtained the similar rules over traditional and idempotent mathematics must not be "parallel''. At first we establish for a compact metric space X the spaces P(X) of probability measures and I(X) idempotent probability measures are homeomorphic ("parallelism''). Then we construct an example which shows that the constructions P and I form distinguished functors from each other ("parallelism'' negation). Further for a compact Hausdorff space X we establish that the hereditary normality of I3(X)\ X implies the metrizability of X.

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来源期刊

Applied general topology MATHEMATICS-

CiteScore

1.20

自引率

25.00%

发文量

审稿时长

15 weeks

期刊介绍： The international journal Applied General Topology publishes only original research papers related to the interactions between General Topology and other mathematical disciplines as well as topological results with applications to other areas of Science, and the development of topological theories of sufficiently general relevance to allow for future applications. Submissions are strictly refereed. Contributions, which should be in English, can be sent either to the appropriate member of the Editorial Board or to one of the Editors-in-Chief. All papers are reviewed in Mathematical Reviews and Zentralblatt für Mathematik.