Lineability

ISBN: 9781138894433 出版年：2015 页码：324 Aron, Richard M Bernal-Gonzalez, Luis Pellegrino, Daniel M CRC Press

We show that there is an infinite-dimensional vector space of differentiable functions on R, every non-zero element of which is nowhere monotone. We also show that there is a vector space of dimension 2 c of functions R → R, every non-zero element of which is everywhere surjective.