Differential Calculus over General Base Fields and Rings

By W. Bertram, Helge Glöckner, Karl-Hermann Neeb. 2004

161 citations recorded by the source corpus.

Abstract We present an axiomatic approach to finite- and infinite-dimensional differential calculus over arbitrary infinite fields (and, more generally, suitable rings). The corresponding basic theory of manifolds and Lie groups is developed. Special attention is paid to the case of mappings between topological vector spaces over non-discrete topological fields, in particular ultrametric fields or the fields of real and complex numbers. In the latter case, a theory of differentiable mappings between general, not necessarily locally convex spaces is obtained, which in the locally convex case is equivalent to Keller's Ckc-theory.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/a002b74df07510785fe58e9d51fa17b2c97a3811

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In Algebra and Number Theory

1. Helge Glöckner
2. Karl-Hermann Neeb
3. W. Bertram
4. Hamza Alzaareer
5. Alexander Schmeding

In Geometry and Topology

1. Helge Glöckner
2. Karl-Hermann Neeb

In Mathematical Physics

1. Helge Glöckner
2. Karl-Hermann Neeb
3. Hamza Alzaareer
4. Alexander Schmeding
5. W. Bertram

Citations in the corpus

• Implicit functions from topological vector spaces to Banach spaces (2003, methodology): “To get from the Banach case to implicit functions on open subsets of metrizable topological vector spaces over a complete ultrametric field ]K, we exploit the fact that a map on a metrizable space is C k if and only if all of its compositions with smooth maps from K k+l to the space are C k [ 2 ].”
• Fundamentals of direct limit Lie theory (2004, background): “Real analytic maps and manifolds in the convenient sense will be called cω R .”