On GSI2-convergence in T0-spaces

In this paper,we introduce the concept of GSI${}_2$-convergence in $T_0$ spaces and the related concept of (strongly) QI${}_2$-continuous spaces. It is proved that if GSI${}_2$-convergence in $X$ is topological iff $X$ is strongly QI${}_2$-continuous for any irreducible complete $T_0$ space $X$.