  In this paper, we prove the following assertion for an absorbing Markov
decision process (MDP) with the given initial distribution, which is also
assumed to be semi-continuous: the continuity of the projection mapping from
the space of strategic measures to the space of occupation measures, both
endowed with their weak topologies, is equivalent to the MDP model being
uniformly absorbing. An example demonstrates, among other interesting
scenarios, that for an absorbing (but not uniformly absorbing) semi-continuous
MDP with the given initial distribution, the space of occupation measures can
fail to be compact in the weak topology.
