  We generalize and extend the Conley-Morse-Forman theory for combinatorial
multivector fields introduced in \cite{Mr2017}. The generalization consists in
dropping the restrictive assumption in \cite{Mr2017} that every multivector has
a unique maximal element. The extension is from the setting of Lefschetz
complexes to the more general situation of finite topological spaces. We define
isolated invariant sets, isolating neighbourhoods, Conley index and Morse
decompositions. We also establish the additivity property of the Conley index
and the Morse inequalities.
