Announcement as effort on topological spaces
  We propose a multi-agent logic of knowledge, public and arbitrary announcements, that is interpreted on topological spaces in the style of subset space semantics. The arbitrary announcement modality functions similarly to the effort modality in subset space logics, however, it comes with intuitive and semantic differences. We provide axiomatizations for three logics based on this setting, and demonstrate their completeness. 
Hans van Ditmarsch, Sophia Knight, Ayb\"uke \"Ozg\"un
cs.LO