{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:29:56Z","timestamp":1760239796904,"version":"build-2065373602"},"reference-count":25,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2020,12,31]],"date-time":"2020-12-31T00:00:00Z","timestamp":1609372800000},"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>This paper aims to mark out new concepts of r-single valued neutrosophic sets, called r-single valued neutrosophic \u00a3-closed and \u00a3-open sets. The definition of \u00a3-single valued neutrosophic irresolute mapping is provided and its characteristic properties are discussed. Moreover, the concepts of \u00a3-single valued neutrosophic extremally disconnected and \u00a3-single valued neutrosophic normal spaces are established. As a result, a useful implication diagram between the r-single valued neutrosophic ideal open sets is obtained. Finally, some kinds of separation axioms, namely r-single valued neutrosophic ideal-Ri (r-SVNIRi, for short), where i={0,1,2,3}, and r-single valued neutrosophic ideal-Tj (r-SVNITj, for short), where j={1,2,212,3,4}, are introduced. Some of their characterizations, fundamental properties, and the relations between these notions have been studied.<\/jats:p>","DOI":"10.3390\/sym13010053","type":"journal-article","created":{"date-parts":[[2020,12,31]],"date-time":"2020-12-31T14:31:49Z","timestamp":1609425109000},"page":"53","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["\u00a3-Single Valued Extremally Disconnected Ideal Neutrosophic Topological Spaces"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3818-3597","authenticated-orcid":false,"given":"Fahad","family":"Alsharari","sequence":"first","affiliation":[{"name":"Department of Mathematics, College of Science and Human Studies, Hotat Sudair, Majmaah University, Majmaah 11952, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,12,31]]},"reference":[{"key":"ref_1","unstructured":"Smarandache, F. (1999). Unifying A Field in Logics, Neutrosophy: Neutrosophic Probability, American Research Press. Set and Logic."},{"key":"ref_2","first-page":"12","article-title":"The category of neutrosophic sets","volume":"14","author":"Hur","year":"2016","journal-title":"Neutrosophic Sets Syst."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"43","DOI":"10.30948\/afmi.2017.14.1.43","article-title":"The category of neutrosophic crisp sets","volume":"14","author":"Hur","year":"2017","journal-title":"Ann. Fuzzy Math. Inform."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"31","DOI":"10.9790\/5728-0343135","article-title":"Neutrosophic set and neutrosophic topological spaces","volume":"3","author":"Salama","year":"2012","journal-title":"IOSR J. Math."},{"key":"ref_5","unstructured":"Salama, A.A., and Smarandache, F. (2015). Neutrosophic Crisp Set Theory, Educational Publisher."},{"key":"ref_6","first-page":"25","article-title":"Neutrosophic crisp sets and neutrosophic crisp topological spaces","volume":"2","author":"Salama","year":"2014","journal-title":"Neutrosophic Sets Syst."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"182","DOI":"10.1016\/0022-247X(68)90057-7","article-title":"Fuzzy topological spaces","volume":"24","author":"Chang","year":"1968","journal-title":"J. Math. Anal. Appl."},{"key":"#cr-split#-ref_8.1","unstructured":"\u0160ostak, A. (1985). On a fuzzy topological structure. Circolo Matematico di Palermo, Palermo"},{"key":"#cr-split#-ref_8.2","unstructured":"Rendiconti del Circolo Matematico di Palermo, Proceedings of the 13th Winter School on Abstract Analysis, Section of Topology, Srni, Czech Republic, 5-12 January 1985, Circolo Matematico di Palermo."},{"key":"ref_9","first-page":"231","article-title":"Base and subbase in intuitionistic I-fuzzy topological spaces","volume":"43","author":"Liang","year":"2014","journal-title":"Hacet. J. Math. Stat."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1007\/s10587-010-0013-7","article-title":"Intuitionistic I-fuzzy topological spaces","volume":"60","author":"Yan","year":"2010","journal-title":"Czechoslov. Math. J."},{"key":"ref_11","first-page":"410","article-title":"Single valued neutrosophic sets","volume":"4","author":"Wang","year":"2010","journal-title":"Multispace Multistruct."},{"key":"ref_12","first-page":"65","article-title":"Smooth neutrosophic topological spaces","volume":"65","year":"2016","journal-title":"Neutrosophic Sets Syst."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Kim, J., Smarandache, F., Lee, J.G., and Hur, K. (2019). Ordinary Single Valued Neutrosophic Topological Spaces. Symmetry, 11.","DOI":"10.3390\/sym11091075"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Saber, Y., Alsharari, F., and Smarandache, F. (2020). On single-valued neutrsophic ideals in \u0160ostak\u2019s sense. Symmetry, 12.","DOI":"10.3390\/sym12020193"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Saber, Y., Alsharari, F., and Smarandache, F. (2020). Connectedness and Stratification of Single-Valued Neutrosophic Topological Spaces. Symmetry, 12.","DOI":"10.3390\/sym12091464"},{"key":"ref_16","first-page":"106","article-title":"Uncertainty assessments of linear time-cost tradeoffs using neutrosophic set","volume":"141","author":"Ali","year":"2020","journal-title":"Comput. Ind. Eng."},{"key":"ref_17","first-page":"964","article-title":"Resource levelling problem in construction projects under neutrosophic environment","volume":"2020 76","author":"Ali","year":"2020","journal-title":"J. Supercomput."},{"key":"ref_18","first-page":"12","article-title":"A Bipolar Neutrosophic Multi Criteria Decision Making Framework for Professional Selection","volume":"10","author":"Gamal","year":"2020","journal-title":"Appl. Sci."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Ubeda, T., and Egenhofer M., J. (2005). Topological error correcting in GIS. Adv. Spat. Databases, 281\u2013297.","DOI":"10.1007\/3-540-63238-7_35"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"411","DOI":"10.1016\/j.laa.2014.07.019","article-title":"Average consensus in multi-agent systems with uncertain topologies and multiple time-varying 443 delays","volume":"459","author":"Shang","year":"2014","journal-title":"Linear Algebra Its Appl."},{"key":"ref_21","unstructured":"Smarandache, F. (2007). A Unifying Field in Logics: Neutrosophic Logic. Neutrosophy, Neutrosophic Set, Neutrosophic Probability and Statistics, InfoLearnQuest. [6th ed.]."},{"key":"ref_22","first-page":"2450","article-title":"A multicriteria decision-making method using aggregation operators for simplified neutrosophic sets","volume":"26","author":"Ye","year":"2014","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1045","DOI":"10.3233\/IFS-151827","article-title":"On single valued neutrosophic relations","volume":"30","author":"Yang","year":"2016","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_24","first-page":"145","article-title":"Decomposition of single-valued neutrosophic ideal continuity via fuzzy idealization","volume":"38","author":"Alsharari","year":"2020","journal-title":"Neutrosophic Sets Syst."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/1\/53\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:48:19Z","timestamp":1760179699000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/1\/53"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,12,31]]},"references-count":25,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2021,1]]}},"alternative-id":["sym13010053"],"URL":"https:\/\/doi.org\/10.3390\/sym13010053","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2020,12,31]]}}}