带邻接零的有限部分等距的局部紧单阵

Q3 Mathematics
O. Gutik, Pavlo Khylynskyi
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引用次数: 3

摘要

摘要设∧是一个由正整数集合∧的偏移α: n∑n +1及其逆偏移β: n +1∑n生成的单oid。证明了如果S是包含Cscr; n的所有正整数部分有限等距的幺正I∞的子幺正I∞的子幺正,则S上的每一个带邻接零的Hausdorff局部紧移连续拓扑要么紧要么离散。我们还证明了具有紧致理想的局部紧致半拓扑半群S也有类似的命题。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
On a locally compact monoid of cofinite partial isometries of ℕ with adjoined zero
Abstract Let 𝒞ℕ be a monoid which is generated by the partial shift α : n↦n +1 of the set of positive integers ℕ and its inverse partial shift β : n + 1 ↦n. In this paper we prove that if S is a submonoid of the monoid Iℕ∞ of all partial cofinite isometries of positive integers which contains Cscr;ℕ as a submonoid then every Hausdorff locally compact shift-continuous topology on S with adjoined zero is either compact or discrete. Also we show that the similar statement holds for a locally compact semitopological semigroup S with an adjoined compact ideal.
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来源期刊
Topological Algebra and its Applications
Topological Algebra and its Applications Mathematics-Algebra and Number Theory
CiteScore
1.20
自引率
0.00%
发文量
12
审稿时长
24 weeks
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