Abstract
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.
Highlights
IntroductionThe Minkowski space is a four-dimensional topological vector space over reals
The Minkowski space is a four-dimensional topological vector space over reals with applications in physical and mathematical sciences [1,2].In general, the Minkowski space is not well behaved if the corresponding Euclidean topological space is considered to be a locally homogeneous space [3]
The multidimensional topological (C, R) space is a non-uniformly scaled quasinormed space admitting a topological group under composite algebraic operations
Summary
The Minkowski space is a four-dimensional topological vector space over reals The Minkowski space is not well behaved if the corresponding Euclidean topological space is considered to be a locally homogeneous space [3]. The reason is that the Minkowski topological space gets decomposed into two locally homogeneous Euclidean subspaces, where the two topological subspaces are separated in nature. Note that the finest topology in n−dimensional Minkowski space is Zeeman topology, which is separable, Hausdorff, locally non-compact, and non-Lindeloff in nature. The n > 1 dimensional Minkowski space equipped with t-topology (Mt ) is not completely Euclidean in nature [4]. The construction of topological fiber space in a non-uniformly scaled quasinormed (C, R) space and the corresponding topological, as well as algebraic analysis of fibration varieties are presented. R, C and Z represent sets of extended real numbers, complex numbers, and integers, respectively
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