Originally Posted by

**measureman** Hi all,

I am working from the following definitions:

Let V be a vector space over a field F. We say that a set C subset V is balanced if for all x in C, ax is in C if |a| <= 1 for a in F. We say that a set C subset V is absorbent if for every x in V; tx is in C for some t > 0.

I am trying to describe these properties geometrically, and I've not found a source that does this. My interepretations are:

Balanced: the set has no isolated points, there are always lots of points around it, it seems a bit like completeness, but not in the usual sense.

Absorbent: A bit like a basis, this set can generate the whole vector space by scalar multiplication.

Does anyone have a better idea?

Thanks.