ultrastrong topology造句

• The adjoint map is not continuous in the ultrastrong topology.
• The weak and strong operator topologies are widely used as convenient approximations to the ultraweak and ultrastrong topologies.
• There is another topology called the ultrastrong * topology, which is the weakest topology stronger than the ultrastrong topology such that the adjoint map is continuous.
• The adjoint map is not continuous in the strong operator and ultrastrong topologies, while the strong * and ultrastrong * topologies are modifications so that the adjoint becomes continuous.
• The ultraweak and ultrastrong topologies are better-behaved than the weak and strong operator topologies, but their definitions are more complicated, so they are usually not used unless their better properties are really needed.