This is an announcement for the paper "Lineability, spaceability, and additivity cardinals for Darboux-like functions" by Krzysztof Chris Ciesielski, Jose L. Gamez-Merino, Daniel Pellegrino, and Juan B. Seoane-Sepulveda.

Abstract: We introduce the concept of {\em maximal lineability cardinal number}, $\mL(M)$, of a subset $M$ of a topological vector space and study its relation to the cardinal numbers known as: additivity $A(M)$, homogeneous lineability $\HL(M)$, and lineability $\LL(M)$ of $M$. In particular, we will describe, in terms of $\LL$, the lineability and spaceability of the families of the following Darboux-like functions on $\real^n$, $n\ge 1$: extendable, Jones, and almost continuous functions.

Archive classification: math.FA

Submitted from: jseoane@mat.ucm.es

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1309.1965

or

http://arXiv.org/abs/1309.1965