Equivariant properties of the space $ {\mathbb Z} (X) $ for a stratifiable space $ X $

In this paper, we prove the action of the compact group $ G $ defined by the stratified space $ X $ is continuous to the space $ Z (X) $ being a stratified space containing the self-stratified space $ X $ as a closed subset. An equivariant analogue of some results of R. Cauty concerning $ A (N) R (S) $ – spaces is proved. It is presented that the orbit space $ Z (X) / G $ by the action of the group $ G $ is a $ S $ space.