论文标题
CECH-COLLETE拓扑组可测量同构的自动连续性
Automatic continuity of measurable homomorphisms on Cech-complete topological groups
论文作者
论文摘要
我们证明，从（本地紧凑的）Cech-Coph-Complete拓扑组$ x $ x $ x $ x $ x $ y $ y $ y $ y $是连续的，并且仅当$ h $可衡量时，并且仅当$ h $是可以普遍衡量的（如果$ h $是可衡量的，则仅当$ h $是haar-h $是haar-measerable）时，$ h：x \ to y $是连续的。这回答了Kuznetsova的一个问题，并扩展了Kleppner在局部紧凑型组之间的同态同态的连续性以及波兰人群之间普遍可测量的同态同态的连续性的结果。
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.
