For a stratified pseudomanifold $X$, we have the de Rham Theorem
$
\lau{\IH}{*}{\per{p}}{X} =
\lau{\IH}{\per{t} - \per{p}}{*}{X},
$
for a perversity $\per{p}$ verifying $\per{0} \leq \per{p} \leq
\per{t}$, where $\per{t}$ denotes the top perversity.
We extend this result to any perversity $\per{p}$. In the direction
cohomology $\mapsto$ homology, we obtain the
isomorphism
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\[
\lau{\IH}{*}{\per{p}}{X} =
\lau{\IH}{\per{t} -\per{p}}{*}{X,\ib{X}{\per{p}}},
\]
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where
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\[
\ib{X}{\per{p}} = \bigcup_{ S \preceq S_{1} \atop
\per{p} (S_{1})< 0}S = \bigcup_{ \per{p} (S)< 0}
\overline{S}.
\]
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In the direction
homology $\mapsto$ cohomology, we obtain the isomorphism
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\[
\lau{\IH}{\per{p}}{*}{X}=\lau{\IH}{*}{\max ( \per{0},\per{t}
-\per{p})}{X}.
\]
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In our paper stratified pseudomanifolds with
one-codimensional strata are allowed.