{'fraction_non_alphanumeric': 0.022494887525562373, 'fraction_numerical': 0.0, 'mean_word_length': 5.363636363636363, '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}}
Local and global continuous -selection

We study properties of sets for which there is a continuous selection from the set of almost-best approximants. We establish relations between local and global selections, give various examples of sets possessing a continuous -selection, and introduce the notions of moduli of approximative continuity, approximative -solarity and uniform approximative continuity. These notions enable us to establish the -solarity of sets under certain conditions.