2026-06-29T02:49:47Zhttps://docta.ucm.es/rest/oai/request

oai:docta.ucm.es:20.500.14352/334352025-04-08T14:36:07Zcom_20.500.14352_14col_20.500.14352_15

On Weierstrass' Monsters and lineability Jiménez Rodríguez, Pablo Muñoz-Fernández, Gustavo A. Seoane Sepúlveda, Juan Benigno 517 lineability spaceability continuous nowhere differentiable function Weierstrass' Monster Análisis matemático 1202 Análisis y Análisis Funcional Let E be a topological vector space and let us consider a property P. We say that the subset M of E formed by the vectors in E which satisfy 2 is mu-lineable (for certain cardinal mu, finite or infinite) if M U {0} contains an infinite dimensional linear space of dimension mu. In 1966 V. Gurariy provided a non-constructive proof of the N-0-lineability of the set of Weierstrass' Monsters (continuous nowhere differentiable functions on R). Here we provide the first constructive proof of the c-lineability of this set (where c denotes the continuum). Of course, this result is the best possible in terms of dimension. Spanish Ministry of Science and Innovation Depto. de Análisis Matemático y Matemática Aplicada Fac. de Ciencias Matemáticas Instituto de Matemática Interdisciplinar (IMI) TRUE pub 2023-06-19T13:22:49Z 2023-06-19T13:22:49Z 2013-12 journal article https://hdl.handle.net/20.500.14352/33435 1370-1444 MTM2009-07848 metadata only access Belgian Mathematical Soc Triomphe