{'fraction_non_alphanumeric': 0.02575107296137339, 'fraction_numerical': 0.001430615164520744, 'mean_word_length': 5.422018348623853, '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}}
A Construction of Analytical Ordered Trapezium Spaces 1

Summary. We define, in a given real linear space, the midpoint operation on vectors and, with the help of the notions of directed parallelism of vectors and orthogonality of vectors, we define the relation of directed trapezium. We consider structures being enrichments of affine structures by a one binary operation, together with a function which assigns to every such structure its ”affine” reduct. Theorems concerning midpoint operation and trapezium relation are proved, which enables us to introduce an abstract notion of (regular in fact) ordered trapezium space with midpoint, ordered trapezium space, and (unordered) trapezium space.