  In this paper, we explore the similarity between normal homogeneity and
$\delta$-homogeneity in Finsler geometry. They are both non-negatively curved
Finsler spaces. We show that any connected $\delta$-homogeneous Finsler space
is $G$-$\delta$-homo-geneous, for some suitably chosen connected quasi-compact
$G$. So $\delta$-homogeneous Finsler metrics can be defined by a bi-invariant
singular metric on $G$ and submersion, just as normal homogeneous metrics,
using a bi-invariant Finsler metric on $G$ instead. More careful analysis
shows, in the space of all Finsler metrics on $G/H$, the subset of all
$G$-$\delta$-homogeneous ones is in fact the closure for the subset of all
$G$-normal ones, in the local $C^0$-topology (Theorem \ref{main-thm-1}). Using
this approximation technique, the classification work for positively curved
normal homogeneous Finsler spaces can be applied to classify positively curved
$\delta$-homogeneous Finsler spaces, which provides the same classification
list. As a by-product, this argument tells more about $\delta$-homogeneous
Finsler metrics satisfying the (FP) condition (a weaker version of positively
curved condition).
