Boolean Representation of Manifolds and Functions
Copyright policy )Boolean Representation of Manifolds and Functions
It is shown that a smooth n dimensional manifold with a boundary in R^n admits a Boolean representation in terms of closed half spaces defined by the tangent hyperplanes at the points on its boundary. A similar result is established for smooth functions on closed convex domains in R^n. The latter result is considered as a form of the Legendre transformation.
6 pages, 1 figure
- San Francisco State University United States
Fuzzy measure theory, Applied Mathematics, representation of manifolds and functions, 26B25, Representation and superposition of functions, Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Legendre transform, Choquet integral, 26B40, Analysis, 26B40; 26B25
Fuzzy measure theory, Applied Mathematics, representation of manifolds and functions, 26B25, Representation and superposition of functions, Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Legendre transform, Choquet integral, 26B40, Analysis, 26B40; 26B25
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