Valuation bases for extensions of valued vector spaces

Let (V,upsilon) be any valued vector space, and (V-0,upsilon) a subspace. Then (V,upsilon) admits a valuation basis over (V-0,upsilon) if and only if it admits a nice composition series over (V-0,upsilon). We show that this is always the case if upsilon(V\V-0) is reversely well ordered. If upsilon(V-0) is reversely well ordered, we show that V-0 is nice in any extension, and that it admits a valuation basis over every subspace. Finally, we show that the property of admitting a valuation basis is preserved under countable dimensional extensions.