One of the nice properties of the first-order logic is the compactness of
satisfiability. It state that a finitely satisfiable theory is satisfiable.
However, different degrees of satisfiability in many-valued logics, poses
various kind of the compactness in these logics. One of this issues is the
compactness of K-satisfiability. Here, after an overview on the results
around the compactness of satisfiability and compactness of K-satisfiability
in many-valued logic based on continuous t-norms (basic logic), we extend the
results around this topic. To this end, we consider a reverse semantical
meaning for basic logic. Then we introduce a topology on [0,1] and [0,1]2
that the interpretation of all logical connectives are continuous with respect
to these topologies. Finally using this fact we extend the results around the
compactness of satisfiability in basic ogic