拓扑半共轭关系是个预序但不是偏序(英文)

The Topological Semi-conjugacy Relation is a Preordering but not a Partial Ordering

本短文指出,存在着紧致连通空间Y及同胚f:Y→Y,g:Y→Y使得f拓扑半共轭于g,g也拓扑半共轭于f,但f与g不拓扑共轭。据此说明了拓扑半共轭关系是个预序但不是偏序。

In this note we indicate that there exist a compact connected space Y and two homeomorphisms / : Y - Y and g : Y - Y such that / is topologically semi-conjugate to g, and g is also topologically semi-conjugate to /, but / and g are not topologically conjugate. Thus, the relation of topological semi-conjugacy is a preordering but not a partial ordering.