{'fraction_non_alphanumeric': 0.022167487684729065, 'fraction_numerical': 0.0, 'mean_word_length': 5.253846153846154, '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}}
Demand continuity and equilibrium in Banach commodity spaces

Norm-to-weak* continuity of excess demand as a function of prices is proved by using our two-topology variant of Berge’s Maximum Theorem. This improves significantly upon an earlier result that, with the extremely strong finite topology on the price space, is of limited interest, except as a vehicle for proving equilibrium existence. With the norm topology on the price space, our demand continuity result becomes useful in applications of equilibrium theory, especially to problems with continuous commodity spectra. Some auxiliary results are also given, including closedness of the total production set and additivity of the asymptotic cone operation. Both are needed in proving equilibrium existence by the use of the Debreu-Gale-Nikaido Lemma.