{'fraction_non_alphanumeric': 0.017676767676767676, 'fraction_numerical': 0.0, 'mean_word_length': 5.007575757575758, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Meyer sets, topological eigenvalues, and Cantor fiber bundles

We introduce two new characterizations of Meyer sets. A repetitive Delone set in ℝd of finite local complexity is topologically conjugate to a Meyer set if and only if it has d linearly independent topological eigenvalues, which is if and only if it is topologically conjugate to a bundle over a d‐torus with totally disconnected compact fiber and expansive canonical action. ‘Conjugate to’ is a non‐trivial condition, as we show that there exist sets that are topologically conjugate to Meyer sets but are not themselves Meyer. We also exhibit a diffractive set that is not Meyer, answering in the negative a question posed by Lagarias, and exhibit a Meyer set for which the measurable and topological eigenvalues are different.