López Gómez, JuliánSampedro Pascual, Juan Carlos2023-06-222023-06-222022-12-211661-773810.1007/s11784-021-00916-7https://hdl.handle.net/20.500.14352/71279CRUE-CSIC (Acuerdos Transformativos 2021)In this paper, we prove an analogue of the uniqueness theorems of Führer [15] and Amann and Weiss [1] to cover the degree of Fredholm operators of index zero constructed by Fitzpatrick, Pejsachowicz and Rabier [13], whose range of applicability is substantially wider than for the most classical degrees of Brouwer [5] and Leray–Schauder [22]. A crucial step towards the axiomatization of this degree is provided by the generalized algebraic multiplicity of Esquinas and López-Gómez [8, 9, 25], χ, and the axiomatization theorem of Mora-Corral [28, 32]. The latest result facilitates the axiomatization of the parity of Fitzpatrick and Pejsachowicz [12], σ(⋅,[a,b]), which provides the key step for establishing the uniqueness of the degree for Fredholm maps.engAtribución 3.0 Españahttps://creativecommons.org/licenses/by/3.0/es/journal articlehttps://doi.org/10.1007/s11784-021-00916-7https://link.springer.com/article/10.1007/s11784-021-00916-7open accessDegree for Fredholm mapsUniquenessAxiomatizationNormalizationgeneralized additivityHomotopy invarianceGeneralized algebraic multiplicityParityOrientabilityÁlgebraLógica simbólica y matemática (Matemáticas)1201 Álgebra1102.14 Lógica Simbólica