Topological Aspects of Differential Chains
| Autor: | Harrison Pugh, Jenny Harrison |
|---|---|
| Rok vydání: | 2011 |
| Předmět: |
FOS: Physical sciences
Mathematical Physics (math-ph) Direct limit Riemannian manifold Space (mathematics) Topology Prime (order theory) Separable space Functional Analysis (math.FA) Mathematics - Functional Analysis Differential geometry FOS: Mathematics Geometry and Topology 57N17 58B10 58A07 58A10 46E99 Mathematical Physics Differential (mathematics) Mackey topology Mathematics |
| DOI: | 10.48550/arxiv.1101.0383 |
| Popis: | In this paper we investigate the topological properties of the space of differential chains 'B(U) defined on an open subset U of a Riemannian manifold M. We show that 'B(U) is not generally reflexive, identifying a fundamental difference between currents and differential chains. We also give several new brief (though non-constructive) definitions of the space 'B(U), and prove that it is a separable ultrabornological (DF)-space. Differential chains are closed under dual versions of fundamental operators of the Cartan calculus on differential forms. The space has good properties some of which are not exhibited by currents B'(U) or D'(U). For example, chains supported in finitely many points are dense in 'B(U) for all open U in M, but not generally in the strong dual topology of B'(U). Comment: 6 pages |
| Databáze: | OpenAIRE |
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