is called positively invariant if
. It is called invariant if
.
is positively invariant, so is
. The
following question arises. Does the invariance of
imply the
invariance of
? If
is a homeomorphism, then the
answer is "yes". The answer is also "yes" if
is compact or if
is compact. However, the
answer in general is "no" 
.
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