SEMITOPOLOGICAL模块

Bukovinian Mathematical Journal Pub Date : 2021-04-14 DOI:10.31861/bmj2021.01.01

T. Banakh, A. Ravsky

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摘要

给定一个拓扑环R，我们研究了半拓扑R模，构造了它们的补全、Bohr和borno修正。对于每一个拓扑空间X，我们构造了X上的自由(半)拓扑r模，并证明了对于k空间X，其自由半拓扑r模是一个拓扑r模。构造了一个自由半拓扑r模不是拓扑r模的Tychono空间X。

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SEMITOPOLOGICAL MODULES

Given a topological ring R, we study semitopological R-modules, construct their completions, Bohr and borno modications. For every topological space X, we construct the free (semi)topological R-module over X and prove that for a k-space X its free semitopological R-module is a topological R-module. Also we construct a Tychono space X whose free semitopological R-module is not a topological R-module.

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Bukovinian Mathematical Journal

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