RT Journal Article
T1 On Weierstrass' Monsters and lineability
A1 Jiménez Rodríguez, Pablo
A1 Muñoz-Fernández, Gustavo A.
A1 Seoane Sepúlveda, Juan Benigno
AB 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.
PB Belgian Mathematical Soc Triomphe
SN 1370-1444
YR 2013
FD 2013-12
LK https://hdl.handle.net/20.500.14352/33435
UL https://hdl.handle.net/20.500.14352/33435
NO Spanish Ministry of Science and Innovation
DS Docta Complutense
RD 17 abr 2025