{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:16:13Z","timestamp":1760238973586,"version":"build-2065373602"},"reference-count":17,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2020,9,21]],"date-time":"2020-09-21T00:00:00Z","timestamp":1600646400000},"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>In this paper, we develop the notion of the basis for a smooth neutrosophic topology in a more natural way. As a sequel, we define the notion of symmetric neutrosophic quasi-coincident neighborhood systems and prove some interesting results that fit with the classical ones, to establish the consistency of theory developed. Finally, we define and discuss the concept of product topology, in this context, using the definition of basis.<\/jats:p>","DOI":"10.3390\/sym12091557","type":"journal-article","created":{"date-parts":[[2020,9,21]],"date-time":"2020-09-21T08:18:01Z","timestamp":1600676281000},"page":"1557","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On Product of Smooth Neutrosophic Topological Spaces"],"prefix":"10.3390","volume":"12","author":[{"given":"Kalaivani","family":"Chandran","sequence":"first","affiliation":[{"name":"Department of Mathematics, Sri Sivasubramaniya Nadar College of Engineering, Kalavakkam 603110, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Swathi Sundari","family":"Sundaramoorthy","sequence":"additional","affiliation":[{"name":"Department of Mathematics, V. V. 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A Unifying Field in Logics, Neutrosophy: Neutrosophic Probability, Set and Logic, American Research Press."},{"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. 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Expos."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"13","DOI":"10.30755\/NSJOM.03237","article-title":"On the product of smooth fuzzy topological spaces","volume":"46","author":"Shakthiganesan","year":"2016","journal-title":"Novi Sad J. Math."},{"key":"ref_11","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_12","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_13","first-page":"410","article-title":"Single valued neutrosophic sets","volume":"4","author":"Wang","year":"2010","journal-title":"Multispace Multistruct."},{"key":"ref_14","first-page":"65","article-title":"Smooth Neutrosophic Topological Spaces","volume":"12","year":"2016","journal-title":"Neutrosophic Sets Syst."},{"key":"ref_15","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_16","doi-asserted-by":"crossref","unstructured":"Al Shumrani, M.A., Gulisten, M., and Smarandache, F. (2020). Further theory of neutrosophic triplet topology and applications. Symmetry, 12.","DOI":"10.3390\/sym12081207"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Saber, Y., Alsharari, F., and Smarandache, F. (2020). On single-valued neutrsophic ideals in \u0160ostak\u2019s sense. 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