  The discovery of topological insulators in non-interacting electron systems
has motivated the community to search such topological states of matter in
correlated electrons both theoretically and experimentally. In this paper we
investigate a phase diagram for a topological Kondo insulating system, where an
emergent "spin"-dependent Kondo effect gives rise to an inversion for
heavy-fermion bands, responsible for a topological Kondo insulator. Resorting
to the U(1) slave-boson mean-field analysis, we uncover an additional phase
transition inside the Kondo insulating state in two dimensions, which results
from the appearance of the topological Kondo insulator. On the other hand, we
observe that the Kondo insulating state is distinguished into three insulating
phases in three dimensions, identified with the weak topological Kondo
insulator, the strong topological Kondo insulator, and the normal Kondo
insulator, respectively, and classified by Z$_{2}$ topological indices. We
discuss the possibility of novel quantum criticality between the fractionalized
Fermi liquid and the topological Kondo insulator, where the band inversion
occurs with the formation of the heavy-fermion band at the same time.
