{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:28:51Z","timestamp":1760239731378,"version":"build-2065373602"},"reference-count":22,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2020,12,10]],"date-time":"2020-12-10T00:00:00Z","timestamp":1607558400000},"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>A holomorphically fibred space generates locally trivial bundles with positive dimensional fibers. This paper proposes two varieties of fibrations (compact and non-compact) in the non-uniformly scalable quasinormed topological (C, R) space admitting cylindrically symmetric continuous functions. The projective base space is dense, containing a complex plane, and the corresponding surjective fiber projection on the base space can be fixed at any point on real subspace. The contact category fibers support multiple oriented singularities of piecewise continuous functions within the topological space. A composite algebraic operation comprised of continuous linear translation and arithmetic addition generates an associative magma in the non-compact fiber space. The finite translation is continuous on complex planar subspace under non-compact projection. Interestingly, the associative magma resists transforming into a monoid due to the non-commutativity of composite algebraic operation. However, an additive group algebraic structure can be admitted in the fiber space if the fibration is a non-compact variety. Moreover, the projection on base space supports additive group structure, if and only if the planar base space passes through the real origin of the topological (C, R) space. The topological analysis shows that outward deformation retraction is not admissible within the dense topological fiber space. The comparative analysis of the proposed fiber space with respect to Minkowski space and Seifert fiber space illustrates that the group algebraic structures in each fiber spaces are of different varieties. The proposed topological fiber bundles are rigid, preserving sigma-sections as compared to the fiber bundles on manifolds.<\/jats:p>","DOI":"10.3390\/sym12122049","type":"journal-article","created":{"date-parts":[[2020,12,10]],"date-time":"2020-12-10T22:15:36Z","timestamp":1607638536000},"page":"2049","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Topological Analysis of Fibrations in Multidimensional (C, R) Space"],"prefix":"10.3390","volume":"12","author":[{"given":"Susmit","family":"Bagchi","sequence":"first","affiliation":[{"name":"Department of Aerospace and Software Engineering (Informatics), Gyeongsang National University, Jinju 660701, Korea"}]}],"member":"1968","published-online":{"date-parts":[[2020,12,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.difgeo.2005.06.006","article-title":"On geometric vector fields of Minkowski spaces and their applications","volume":"24","author":"Vincze","year":"2006","journal-title":"Differ. Geom. Its Appl."},{"key":"ref_2","first-page":"129","article-title":"Application of Minkowski space to description of anisotropic pore space structure in porous materials","volume":"80","author":"Cleszko","year":"2011","journal-title":"Suppl. Minisymp. Math. Mech."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"49","DOI":"10.5937\/MatMor1501049E","article-title":"Generalized open sets of Minkowski space","volume":"19","author":"Ersoy","year":"2015","journal-title":"Math. Moravica"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1063\/1.3129188","article-title":"t-topology on the n-dimensional Minkowski space","volume":"50","author":"Agrawal","year":"2009","journal-title":"J. Math. Phys."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Guler, E. (2020). Helical hypersurfaces in Minkowski geometry E14. Symmetry, 12.","DOI":"10.3390\/sym12081206"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"57","DOI":"10.4064\/fm-61-1-57-72","article-title":"On bundles over a sphere with fiber Euclidean space","volume":"61","author":"Wall","year":"1967","journal-title":"Fundam. Math."},{"key":"ref_7","first-page":"694106","article-title":"A survey on Seifert fiber space theorem","volume":"2014","author":"Preaux","year":"2014","journal-title":"ISRN Geom."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1007\/s10711-016-0209-6","article-title":"Profinite rigidity for Seifert fiber spaces","volume":"188","author":"Wilkes","year":"2017","journal-title":"Geom. Dedicata"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"4057","DOI":"10.1090\/S0002-9947-05-03804-3","article-title":"Scott\u2019s rigidity theorem for Seifert fibered spaces; Revisited","volume":"358","author":"Soma","year":"2006","journal-title":"Trans. Am. Math. Soc."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1017\/S0305004100073527","article-title":"A rigidity theorem for Haken manifolds","volume":"118","author":"Soma","year":"1995","journal-title":"Math. Proc. Camb. Philos. Soc."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1016\/j.geomphys.2013.10.005","article-title":"On the geometry of null hypersurfaces in Minkowski space","volume":"75","author":"Navarro","year":"2014","journal-title":"J. Geom. Phys."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"231","DOI":"10.4310\/jdg\/1214439564","article-title":"3-dimensional Lorentz space-forms and Seifert fiber spaces","volume":"21","author":"Kulkarni","year":"1985","journal-title":"J. Differ. Geom."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"562","DOI":"10.2307\/1970156","article-title":"On the immersion of manifolds in Euclidean space","volume":"68","author":"Lashof","year":"1958","journal-title":"Ann. Math."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1063\/1.168345","article-title":"A visualization model based on the mathematics of fiber bundles","volume":"3","author":"Butler","year":"1989","journal-title":"Comput. Phys."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"256","DOI":"10.2307\/1969542","article-title":"The equivalence of fiber bundles","volume":"53","author":"Hu","year":"1951","journal-title":"Ann. Math."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Bagchi, S. (2020). On the topological structure and properties of multidimensional (C, R) space. Symmetry, 12.","DOI":"10.3390\/sym12091542"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"394","DOI":"10.1063\/1.1665602","article-title":"Topology for Minkowski space","volume":"12","author":"Nanda","year":"1971","journal-title":"J. Math. Phys."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1142\/S0129167X14500062","article-title":"Rigidity of holomorphic maps between fiber spaces","volume":"25","author":"Bharali","year":"2014","journal-title":"Int. J. Math."},{"key":"ref_19","first-page":"71","article-title":"Fiber bundles with singularities","volume":"18","author":"Church","year":"1968","journal-title":"J. Math. Mech."},{"key":"ref_20","unstructured":"Marathe, K.B. (1970). Minkowski spaces as fiber bundles. C.I.M.E. Bolzano Italy, Springer."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1016\/0040-9383(67)90033-X","article-title":"The topology of Minkowski space","volume":"6","author":"Zeeman","year":"1967","journal-title":"Topology"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1017\/S0027763000013325","article-title":"On the automorphism group of a holomorphic fiber bundle over a complex space","volume":"37","author":"Fujimoto","year":"1970","journal-title":"Nagoya Math J."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/12\/2049\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:43:34Z","timestamp":1760179414000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/12\/2049"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,12,10]]},"references-count":22,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2020,12]]}},"alternative-id":["sym12122049"],"URL":"https:\/\/doi.org\/10.3390\/sym12122049","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2020,12,10]]}}}