Acta Mathematica Vietnamica
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THE INHERITANCE OF THE LINEAR TOPOLOGICAL INVARIANT $(DN)$
DINH HUY HOANG, THAI THUAN QUANG
Abstract
It is shown that if $X$ is a Stein space and $S$ is a closed set in $X$ with $H_{2\dim\, X-1}(S) = 0$, then $H(X)\in (DN)$ if and only if $H(X\backslash S) \in (DN)$. Moreover it is also shown that the property $(DN)$ is invariant under holomorphic surjections between Stein spaces with connected fibres having the property $(DN)$.