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arxiv: 1511.01046 · v1 · pith:AUNGEBLMnew · submitted 2015-11-02 · 🧮 math.GN · math.CO· math.GR

Box Resolvability

classification 🧮 math.GN math.COmath.GR
keywords kapparesolvablegrouptopologicalinfinitepartiallysubsetthen
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We say that a topological group $G$ is partially box $\kappa$-resolvable if there exist a dense subset $B$ of $G$ and a subset $A $ of $G$, $|A|=\kappa$ such that the subsets $\{ aB: a\in A\}$ are pairwise disjoint. If $G=AB$ then $G$ is called box $\kappa$-resolvable. We prove two theorems. If a topological group $G$ contains an injective convergent sequence then $G$ is box $\omega$-resolvable. Every infinite totally bounded topological group $G$ is partially box $n$-resolvable for each natural number $n$, and $G$ is box $\kappa$-resolvable for each infinite cardinal $\kappa, \kappa<|G|$.

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