Jiménez Rodríguez, PabloMuñoz-Fernández, Gustavo A.Seoane-Sepúlveda, Juan B.2023-06-202023-06-202012-08-150024-379510.1016/j.laa.2012.04.010https://hdl.handle.net/20.500.14352/42298Let 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 P is μ-lineable (for certain cardinal μ, finite or infinite) if M ∪ {0} contains an infinite dimensional linear space of dimension μ. In this note we prove that there exist uncountably infinite dimensional linear spaces of functions enjoying the following properties:(1) Being continuous on [0, 1], a.e. differentiable, with a.e. bounded derivative, and not Lipschitz. (2) Differentiable in (R2)R and not enjoying the Mean Value Theorem. (3) Real valued differentiable on an open, connected, and non-convex set, having bounded gradient,non-Lipschitz, and (therefore) not verifying the Mean Value Theorem.engjournal articlehttp://www.sciencedirect.com/science/article/pii/S0024379512002741#http://www.sciencedirect.com/restricted access517LineabilitySpaceabilityContinuous non-LipschitzfunctionsMean Value TheoremAnálisis matemático1202 Análisis y Análisis Funcional