SI2-TOPOLOGY ON T0 SPACES

This paper provides a new approach to defining a topology by
using irreducible sets from a given T0 space. This derived topology, called
SI2-topology, leads to a weak sobriety and continuity, called δ-sobriety and
SI2-continuity, respectively. It is proved that the δ-sober C-spaces are ex-
actly the s2-topological spaces on s2-continuous posets. Moreover, it turns
out that the SI2-topology on a T0 space can be described completely in terms
of convergence, and this convergence structure is topological whenever the
given space is SI2-continuous.