In this paper, we give some characterizations of
$\delta$-stratifiable spaces by means of $g$-functions and semi-continuous
functions. It is established that:
ıtem{(1)} A topological space $X$ in which every point is a regular
$G_\delta$-set is $\delta$-stratifiable if and only if there
exists a $g$-function $g:N\times X\rightarrow \tau $ satisfies
that if $F\in RG(X)$ and $y\notin F$, then there is an $m\in N$
such that $y\notin \overline{g(m,F)}$;
ıtem{(2)} If there is an order preserving map $\varphi:USC(X)\rightarrow LSC(X) $ such
that for any $h\in USC(X),0\leq \varphi(h)\leq h$ and
$0<\varphi(h)(x)