Tautness and applications of the Alexander-Spanier cohomology of \(K\)-types (Q5945181)

The authors prove that the \textit{K}-Alexander-Spanier cohomology of a closed subset in a paracompact space is isomorphic to the direct limit of the \textit{K}-Alexander-Spanier cohomology of its neighborhoods. Also, it is proved that the partially continuous \textit{K}-Alexander-Spanier cohomology of a neighborhood retract closed subspace of a Hausdorff space is isomorphic to the direct limit of the partially continuous \textit{K}-Alexander-Spanier cohomology of its neighborhoods. A version of the continuity property is proved, and some applications are given.