Teoremas Banach-Stone en espacios métricos
- Cabello Sánchez, Javier
- Félix Cabello Sánchez Zuzendaria
Defentsa unibertsitatea: Universidad de Extremadura
Fecha de defensa: 2014(e)ko urria-(a)k 24
- Jesús Angel Jaramillo Aguado Presidentea
- Antonio Ángel Pulgarín García Idazkaria
- Antonio Jiménez Vargas Kidea
- Francisco Montalvo Durán Kidea
- María Isabel Garrido Carballo Kidea
Mota: Tesia
Laburpena
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.