For a real vector space E, the second author introduced the locally convex topology T in [15] such that (E, T) is the strongest locally convex topology contained in the finite topology. In this paper, we shall prove the following.
(1) (E, T) is a σ-metric stratifiable space.
(2) For any σ-metric stratifiable space X, X can be embedded in a AR (σ-metric stratifiable)-space as a closed subset.
(3) For each natural number n, the fundamental subspace E_n of (E , T) is AE(stratifiable).
(4) For any σ-metric stratifiable space X, X is AR(σ-metric stratifiable) (resp. ANR) if and only if X is AE(σ-metric stratifiable) (resp. ANE).