additional property: hypocontinuity. All continuous bilinear maps are hypocontinuous. Many bilinear maps that occur in practice are separately continuous...

In mathematics, a hypocontinuous is a condition on bilinear maps of topological vector spaces that is weaker than continuity but stronger than separate...

differentiation map C c ∞ ( U ) → C c ∞ ( U ) {\displaystyle C_{c}^{\infty }(U)\to C_{c}^{\infty }(U)} is a continuous linear operator. The bilinear multiplication...

separately continuous bilinear map from a product of barrelled spaces into a locally convex space is hypocontinuous. A linear map with a closed graph from...

to be continuous. Each of these non-continuous maps is, however, separately continuous and hypocontinuous. In general, regularity is required for multiplication...