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تسجيل مستخدم جديدConnected neighborhoods in Cartesian products of solenoids
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Given a collection of pairwise co-prime integers $% m_{1},ldots ,m_{r}$, greater than $1$, we consider the product $Sigma =Sigma _{m_{1}}times cdots times Sigma _{m_{r}}$, where each $Sigma _{m_{i}}$ is the $m_{i}$-adic solenoid. Answering a question of D. P. Bellamy and J. M. L ysko, in this paper we prove that if $M$ is a subcontinuum of $Sigma $ such that the projections of $M$ on each $Sigma _{m_{i}}$ are onto, then for each open subset $U$ in $Sigma $ with $Msubset U$, there exists an open connected subset $V$ of $Sigma $ such that $Msubset Vsubset U$; i.e. any such $M$ is ample in the sense of Prajs and Whittington [10]. This contrasts with the property of Cartesian squares of fixed solenoids $Sigma _{m_{i}}times Sigma _{m_{i}}$, whose diagonals are never ample [1].
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