In mathematics, a hypocontinuous is a condition on
bilinear maps of
topological vector spaces that is weaker than continuity but stronger than
separate continuity. Many important bilinear maps that are not continuous are, in fact, hypocontinuous.
for every bounded set the set of linear maps is an equicontinuous subset of .
Sufficient conditions
Theorem:[1] Let X and Y be
barreled spaces and let Z be a
locally convex space. Then every separately continuous bilinear map of into Z is hypocontinuous.
In mathematics, a hypocontinuous is a condition on
bilinear maps of
topological vector spaces that is weaker than continuity but stronger than
separate continuity. Many important bilinear maps that are not continuous are, in fact, hypocontinuous.
for every bounded set the set of linear maps is an equicontinuous subset of .
Sufficient conditions
Theorem:[1] Let X and Y be
barreled spaces and let Z be a
locally convex space. Then every separately continuous bilinear map of into Z is hypocontinuous.