具有独立连续马尔采夫操作的自由拓扑代数

IF 0.6 4区数学 Q3 MATHEMATICS

Functional Analysis and Its Applications Pub Date : 2024-04-01 DOI:10.1134/s001626632304007x

O. V. Sipacheva, A. A. Solonkov

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引用次数: 0

摘要

摘要研究了具有单独连续的 Mal'tsev 操作的拓扑空间，称为准 Mal'tsev 空间。证明了由任意完全规则的 Hausdorff 空间生成的自由准 Mal'tsev 空间的存在性。证明了任何准马尔采夫空间都是自由准马尔采夫空间的商。同时还证明了自由准马尔采夫空间的拓扑学在生成空间方面有着简单而自然的描述。最后，证明了任何完全正则的准马尔泰夫空间都是准拓扑群的retract。

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Free Topological Algebra with Separately Continuous Mal’tsev Operation

Abstract

Topological spaces with separately continuous Mal’tsev operation, called quasi-Mal’tsev spaces, are considered. The existence of the free quasi-Mal’tsev space generated by an arbitrary completely regular Hausdorff space is proved. It is shown that any quasi-Mal’tsev space is a quotient of a free quasi-Mal’tsev space. It is also shown that the topology of a free quasi-Mal’tsev space has a simple and natural description in terms of the generating space. Finally, it is proved that any completely regular Hausdorff quasi-Mal’tsev space is a retract of a quasi-topological group.

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来源期刊

Functional Analysis and Its Applications 数学-数学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Functional Analysis and Its Applications publishes current problems of functional analysis, including representation theory, theory of abstract and functional spaces, theory of operators, spectral theory, theory of operator equations, and the theory of normed rings. The journal also covers the most important applications of functional analysis in mathematics, mechanics, and theoretical physics.