Dugundji Compacta and the Space of Idempotent Probability Measures

For a given group of topological transformations on a Tikhonov space , a group of topological transformations on the space of idempotent probability measures is constructed. It is shown that, if the action of the group is open, then the action of the group is also open; while an example is given showing that the openness of the action is substantial. It has been established that, if the diagonal product of a given family of continuous mappings is an embedding, then the diagonal product of the family of continuous mappings is also an embedding. A Dugundji compactness criterion for the space of idempotent probability measures is obtained.