Generalizations of Topological Decomposition and Zeno Sequence in Fibered n-Spaces

Abstract

The space-time geometry is rooted in the Minkowski 4-manifold. Minkowski and Euclidean topological 4-manifolds behave differently in view of compactness and local homogeneity. As a result, Zeno sequences are selectively admitted in such topological spaces. In this paper, the generalizations of topologically fibered n-spaces are proposed to formulate topological decomposition and the formation of projective fibered n-subspaces. The concept of quasi-compact fibering is introduced to analyze the formation of Zeno sequences in topological n-spaces (i.e., n-manifolds), where a quasi-compact fiber relaxes the Minkowski-type (algebraically) strict ordering relation under topological projections. The topological analyses of fibered Minkowski as well as Euclidean 4-spaces are presented under quasi-compact fibering and topological projections. The topological n-spaces endowed with quasi-compact fibers facilitated the detection of local as well as global compactness and the non-analytic behavior of a continuous function. It is illustrated that the 5-manifold with boundary embedding Minkowski 4-space transformed a quasi-compact fiber into a compact fiber maintaining generality.