Azagra Rueda, Daniel2023-06-202023-06-2019970039-3223https://hdl.handle.net/20.500.14352/57010We prove that for every infinite-dimensional Banach space X with a Frechet differentiable norm, the sphere S-X is diffeomorphic to each closed hyperplane in X. We also prove that every infinite-dimensional Banach space Y having a (not necessarily equivalent) C-p norm (with p is an element of N boolean OR {infinity}) is C-p diffeomorphic to Y \ {0}.engjournal articlehttp://journals.impan.gov.pl/sm/http://matwbn.icm.edu.pl/spis.php?wyd=2open access517.986Infinite-dimensional Banach spaceUnit sphereHyperplaneDiffeomorphismFunciones (Matemáticas)1202 Análisis y Análisis Funcional