论文标题
几何瓷砖：距离，拓扑，紧凑和完整性
Geometrical tilings : distance, topology, compactness and completeness
论文作者
论文摘要
我们介绍了文献中存在的RD斜利的不同距离，我们证明（大多数）这些定义是正确的（即它们确实定义了RD瓷砖的指标）。我们证明，对于具有有限局部复杂性（FLC）的次班，这些指标在拓扑上是等效的，甚至在指标上等效，并且我们也提出了紧凑性和完整性的经典结果。请注意，除了这些指标的等效性外，此处介绍的所有结果都是已知的（例如，请参见调查[ROB04]），但是我们无法找到其中一些结果的完整证明的参考，因此我们决定编写此通知以阐明某些定义并提供完整的证明。
We present the different distances on tilings of Rd that exist in the literature, we prove that (most of) these definitions are correct (i.e. they indeed define metrics on tilings of Rd ). We prove that for subshifts with finite local complexity (FLC) these metrics are topologically equivalent and even metrically equivalent, and also we present classical results of compactness and completeness. Note that, excluding the equivalence of these metrics, all of the results presented here are known (see for example the survey [Rob04]) however we were unable to find a reference with complete proofs for some of these results so we decided to write this notice to clarify some definitions and give full proofs.
