Extremally $T_1$-spaces and Related Spaces
  The aim of this paper is introduce and initiate the study of extremally $T_1$-spaces, i.e., the spaces where all hereditarily compact $C_2$-subspaces are closed. A $C_2$-space is a space whose nowhere dense sets are finite. 
Julian Dontchev, Maximilian Ganster and Laszlo Zsilinszky