{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,15]],"date-time":"2026-01-15T04:32:55Z","timestamp":1768451575735,"version":"3.49.0"},"reference-count":28,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2020,9,7]],"date-time":"2020-09-07T00:00:00Z","timestamp":1599436800000},"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 introduce the notion of r-single-valued neutrosophic connected sets in single-valued neutrosophic topological spaces, which is considered as a generalization of r-connected sets in \u0160ostak\u2019s sense and r-connected sets in intuitionistic fuzzy topological spaces. In addition, it introduces the concept of r-single-valued neutrosophic separated and obtains some of its basic properties. It also tries to show that every r-single-valued neutrosophic component in single-valued neutrosophic topological spaces is an r-single-valued neutrosophic component in the stratification of it. Finally, for the purpose of symmetry, it defines the so-called single-valued neutrosophic relations.<\/jats:p>","DOI":"10.3390\/sym12091464","type":"journal-article","created":{"date-parts":[[2020,9,7]],"date-time":"2020-09-07T09:18:16Z","timestamp":1599470296000},"page":"1464","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Connectedness and Stratification of Single-Valued Neutrosophic Topological Spaces"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4795-3469","authenticated-orcid":false,"given":"Yaser","family":"Saber","sequence":"first","affiliation":[{"name":"Department of Mathematics, College of Science and Human Studies, Hotat Sudair, Majmaah University, Majmaah 11952, Saudi Arabia"},{"name":"Department of Mathematics, Faculty of Science Al-Azhar University, Assiut 71524, Egypt"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3818-3597","authenticated-orcid":false,"given":"Fahad","family":"Alsharari","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science and Human Studies, Hotat Sudair, Majmaah University, Majmaah 11952, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5560-5926","authenticated-orcid":false,"given":"Florentin","family":"Smarandache","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of New Mexico, Gallup, NM 87301, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1228-3821","authenticated-orcid":false,"given":"Mohammed","family":"Abdel-Sattar","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science and Arts King Khaled University, Mhayal Asier 61913, Saudi Arabia"},{"name":"Department of Mathematics and Computer Science, Faculty of Science, Beni-Suef University, Beni-Suef 62511, Egypt"}]}],"member":"1968","published-online":{"date-parts":[[2020,9,7]]},"reference":[{"key":"ref_1","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_2","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1016\/S0165-0114(86)80034-3","article-title":"Intuitionistic fuzzy sets","volume":"20","author":"Atanassov","year":"1986","journal-title":"Fuzzy Sets Syst."},{"key":"ref_3","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":"ref_4","doi-asserted-by":"crossref","first-page":"621","DOI":"10.1016\/0022-247X(76)90029-9","article-title":"Fuzzy topological spaces and fuzzy compactness","volume":"56","author":"Lowen","year":"1976","journal-title":"J. Math. Anal. Appl."},{"key":"ref_5","first-page":"161","article-title":"Mated fuzzy topological spaces","volume":"11","author":"Lee","year":"2001","journal-title":"Int. J. Fuzzy Log. Intell. Syst."},{"key":"ref_6","unstructured":"Liu, Y.M., and Luo, M.K. (1997). Fuzzy Topology, World Scientific Publishing Co."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1016\/0165-0114(93)90277-O","article-title":"Fuzzy topology: Fuzzy closure operator, fuzzy compactness and fuzzy connectedness","volume":"54","author":"Chattopadhyay","year":"1993","journal-title":"Fuzzy Sets Syst."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1016\/0165-0114(92)90329-3","article-title":"Gradation of openness: Fuzzy topology","volume":"49","author":"Chattopadhyay","year":"1992","journal-title":"Fuzzy Sets Syst."},{"key":"ref_9","first-page":"233","article-title":"Connectedness on fuzzy topological spaces","volume":"20","author":"Zhao","year":"1986","journal-title":"Fuzzy Sets Syst."},{"key":"ref_10","first-page":"1667","article-title":"Ideals on fuzzy topological spaces","volume":"8","author":"Saber","year":"2014","journal-title":"Appl. Math. Sci."},{"key":"#cr-split#-ref_11.1","unstructured":"\u0160ostak, A. (1985). On a fuzzy topological structure. Circolo Matematico di Palermo, Palermo"},{"key":"#cr-split#-ref_11.2","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_12","unstructured":"Smarandache, F. (1998). Neutrosophy, Neutrisophic Property, Sets, and Logic, American Research Press."},{"key":"ref_13","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_14","unstructured":"Salama, A.A., and Smarandache, F. (2015). Neutrosophic Crisp Set Theory, The Educational Publisher Columbus."},{"key":"ref_15","first-page":"410","article-title":"Single valued neutrosophic sets","volume":"4","author":"Wang","year":"2010","journal-title":"Multispace Multistruct."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"201","DOI":"10.30948\/afmi.2018.16.2.201","article-title":"Single valued neutrosophic relations","volume":"16","author":"Kim","year":"2018","journal-title":"Ann. Fuzzy Math. Inform."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Saber, Y.M., Alsharari, F., and Smarandache, F. (2020). On single-valued neutrosophic ideals in \u0160ostak sense. Symmetry, 12.","DOI":"10.3390\/sym12020193"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1007\/3-540-63238-7_35","article-title":"Topological error correcting in GIS","volume":"1262","author":"Ubeda","year":"1997","journal-title":"Adv. Spat. Databases"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"2397","DOI":"10.1016\/S0960-0779(00)00108-9","article-title":"On the unification of heterotic strings, M theory and \u2130\u221e theory","volume":"11","year":"2000","journal-title":"Chaos Solitons Fractals"},{"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 delays","volume":"459","author":"Shang","year":"2014","journal-title":"Linear Algebra 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","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_23","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_24","first-page":"65","article-title":"Smooth neutrosophic topological spaces","volume":"65","year":"2016","journal-title":"Neutrosophic Sets Syst."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Alsharari, F. (2020). Decomposition of single-valued neutrosophic ideal continuity via fuzzy idealization. Neutrosophic Sets Syst., under revision.","DOI":"10.3390\/sym13081508"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1007\/BF01332770","article-title":"A topological notion of boundedness","volume":"10","author":"Lambrinos","year":"1973","journal-title":"Manuscr. Math."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.ins.2004.05.002","article-title":"Fuzzy L-bornological spaces","volume":"173","author":"Yan","year":"2005","journal-title":"Inf. Sci."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/9\/1464\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:07:28Z","timestamp":1760177248000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/9\/1464"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,9,7]]},"references-count":28,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2020,9]]}},"alternative-id":["sym12091464"],"URL":"https:\/\/doi.org\/10.3390\/sym12091464","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,9,7]]}}}