Cech-完全的拓扑群上可测同态的自动连续性
Automatic continuity of measurable homomorphisms on Cech-complete topological groups
摘要：
证明了从（局部紧）Cech-完全的拓扑群$X$到拓扑群$Y$的同态$h:X\to Y$是连续的当且仅当$h$是Borel-可测的当且仅当$h$是泛可测的（当且仅当$h$是Haar-可测的）.这回答了库兹涅佐娃的问题，并延长了结果Kleppner的连续性Haar可测同态之间的局部紧群和结果Rosendal的连续性普遍可测同态之间的波兰团体。
英文摘要：
We prove that a homomorphism $h:X\to Y$ from a (locally compact) Cech-complete topological group $X$ to a topological group $Y$ is continuous if and only if $h$ is Borel-measurable if and only if $h$ is universally measurable (if and only if $h$ is Haar-measurable). This answers a problem of Kuznetsova and extends a result of Kleppner on the continuity of Haar-measurable homomorphisms between locally compact groups and a result of Rosendal on the continuity of universally measurable homomorphisms between Polish groups.
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