I'm reading "L'hypothèse du continu" by Sierpinski. He mentions many time "ensembles linéaires" or "linear sets" without defining this notion. Does anyone know what is the definition a such a set ?
Here is a translation into english of 2 proposition he gave :
"There exist a linear set whose cardinality is that of the continuum and whose image by any continuous function is of measure zero".
"There exist a linear set whose cardinality is that of the continuum and whose homeomorphic images have the same measure".