  In \cite{E_2018}, Ern\'e relaxed the concept of sobriety in order to extend
the theory of sober spaces and locally hypercompact spaces to situations where
directed joins were missing, and introduced three kinds of non-sober spaces:
cut spaces, weakly sober spaces, and quasisober spaces. In this paper, their
basic properties are investigated. It is shown that some properties which are
similar to that of sober spaces hold and others do not hold.
