Abstract:We obtain some new properties of the class of KC-spaces, that is, those topological spaces in which compact sets are closed. The results are used to generalize theorems of Anderson [1] and Steiner and Steiner [12] concerning complementation in the lattice of $T_1$-topologies on a set $X$.
Keywords: KC-space, $T_1$-complementary topology, $T_1$-independent, sequential space
AMS Subject Classification: Primary 54A10; Secondary 54D10, 54D25, 54D55