{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,23]],"date-time":"2026-01-23T08:08:34Z","timestamp":1769155714250,"version":"3.49.0"},"reference-count":24,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2022,4,29]],"date-time":"2022-04-29T00:00:00Z","timestamp":1651190400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>As daily problems involve a great deal of data and ambiguity, it has become vital to build new mathematical ways to cope with them, and soft set theory is the greatest tool for doing so. As a result, we study methods of generating soft topologies through several soft set operators. A soft topology is known to be determined by the system of special soft sets, which are called soft open (dually soft closed) sets. The relationship between specific types of soft topologies and their classical topologies (known as parametric topologies) is linked to the idea of symmetry. Under this symmetry, we can study the behaviors and properties of classical topological concepts via soft settings and vice versa. In this paper, we show that soft topological spaces can be characterized by soft closure, soft interior, soft boundary, soft exterior, soft derived set, or co-derived set operators. All of the soft topologies that result from such operators are equivalent, as well as being identical to their classical counterparts under enriched (extended) conditions. Moreover, some of the soft topologies are the systems of all fixed points of specific soft operators. Multiple examples are presented to show the implementation of these operators. Some of the examples show that, by removing any axiom, we will miss the uniqueness of the resulting soft topology.<\/jats:p>","DOI":"10.3390\/sym14050914","type":"journal-article","created":{"date-parts":[[2022,5,4]],"date-time":"2022-05-04T08:21:25Z","timestamp":1651652485000},"page":"914","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":32,"title":["Generating Soft Topologies via Soft Set Operators"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1206-9326","authenticated-orcid":false,"given":"A. A.","family":"Azzam","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science and Humanities, Prince Sattam Bin Abdulaziz University, Alkharj 11942, Saudi Arabia"},{"name":"Department of Mathematics, Faculty of Science, New Valley University, Elkharga 72511, Egypt"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0740-3331","authenticated-orcid":false,"given":"Zanyar A.","family":"Ameen","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, University of Duhok, Duhok 42001, Iraq"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8074-1102","authenticated-orcid":false,"given":"Tareq M.","family":"Al-shami","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Sana\u2019a University, Sana\u2019a P.O. Box 1247, Yemen"}]},{"given":"Mohammed E.","family":"El-Shafei","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt"}]}],"member":"1968","published-online":{"date-parts":[[2022,4,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1016\/S0898-1221(99)00056-5","article-title":"Soft set theory\u2014First results","volume":"37","author":"Molodtsov","year":"1999","journal-title":"Comput. Math. Appl."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"338","DOI":"10.1016\/S0019-9958(65)90241-X","article-title":"Fuzzy sets","volume":"8","author":"Zadeh","year":"1965","journal-title":"Inf. Control"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1007\/BF01001956","article-title":"Rough sets","volume":"11","author":"Pawlak","year":"1982","journal-title":"Int. J. Comput. Inf. 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