Hyper-Continuous Space Theory: A Generalized Framework for Higher-Order Continuity and Multi-Scale Topological Structures
Year: 2026
Type: preprint
Abstract: This paper introduces the Hyper-Continuous Space Theory (HCST) as a generalized mathematical framework designed to transcend the limitations of traditional manifold and topological theories. By formalizing a parameterized space denoted as C^(alpha, beta, gamma), the theory captures higher-order recursive smoothness, fractal-topological density, and nonlocal informational connectivity. We establish the foundational axioms of hyper-continuity, develop the algebraic and analytical apparatus including hyper-differential operators, and formulate generalized variational principles and wave equations. Furthermore, we demonstrate how HCST provides a robust mechanism for resolving singularity bottlenecks and embeds classical spaces as degenerate subclasses through functorial mappings, opening new avenues for advanced theoretical modeling without reliance on experimental constraints.
Author: Zhang, Jincheng
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7196966663