{'fraction_non_alphanumeric': 0.01870503597122302, 'fraction_numerical': 0.0, 'mean_word_length': 4.612903225806452, '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}}
Soft sets over a common topological universe

Although works on soft set theory have been studied in various directions by many researchers, in this paper, we investigate soft set theory in new methods which are different from the old. First, we introduce the notion of topological universe, which is a special universe having a topology defined on the given universe. The reason why we introduce the notion is to define new soft sets by using the notion. The defined new soft sets will be called quasi-open soft sets and open soft sets, and we will study some basic properties. Furthermore, we will investigate several types of soft functions preserving quasi-open soft sets and open soft sets.