Teoremas Banach-Stone en espacios métricos
- Cabello Sánchez, Javier
- Félix Cabello Sánchez Director/a
Universitat de defensa: Universidad de Extremadura
Fecha de defensa: 24 de d’octubre de 2014
- Jesús Angel Jaramillo Aguado President
- Antonio Ángel Pulgarín García Secretari/ària
- Antonio Jiménez Vargas Vocal
- Francisco Montalvo Durán Vocal
- María Isabel Garrido Carballo Vocal
Tipus: Tesi
Resum
In this work we deal with spaces of continuous, uniformly continuous, Lipschitz and differentiable functions. We consider order isomorphisms between function spaces and also multiplicative isomorphisms. We will show that we can always find a homeomorphism between the underlying spaces and represent these isomorphisms pointwise. Two of the main results are the following: • Theorem: Let X and Y be complete metric spaces. Every order isomorphism T : U(Y) →U(X) is Tf(x) = t(x, f(τ (x))), where t : (x, c) ϵ X x R → t(x, c) = Tc(x) and τ is a uniform homeomorphism between X and Y. • Theorem: Let X and Y be finite dimensional class k differentiable manifolds. Every multiplicative isomorphism T : Cᵏ (Y) → Cᵏ (X) arises as Tf(x) = f(τ (x)), for some class k diffeomorphism τ : X → Y.