论文标题
遗传性不可分解的连续性作为通用数学结构
Hereditarily indecomposable continua as generic mathematical structures
论文作者
论文摘要
我们将伪弧以及P-Adic伪螺旋体（对于一组Primes P）描述为通用结构，这是由自然游戏引起的，其中两个玩家在建立倒数的反向序列时交替出现。如果此序列的极限是同构的，则第二名球员会获胜，因为每当第二个玩家有胜利策略时，都称为通用空间（提前固定）。 为此，我们开发了一种新的近似fraïssé理论，以实现上述对象（伪 - arc和伪 - 六叶素）作为fraïssé限制。我们的框架扩展了经典和投影的离散式弗拉西斯理论，也适合直接与可迁移的紧凑型持续地图合作。 我们特别表明，在非排分Peano Continua之间进行连续冲销时，伪弧总是通用的。在圆形连续图之间的所有冲销中，通用的伪六丝氨酸似乎是通用的。
We characterize the pseudo-arc as well as P-adic pseudo-solenoids (for a set of primes P) as generic structures, arising from a natural game in which two players alternate in building an inverse sequence of surjections. The second player wins if the limit of this sequence is homeomorphic to a concrete (fixed in advance) space, called generic whenever the second player has a winning strategy. For this aim, we develop a new approximate Fraïssé theory, in order to realize the above-mentioned objects (the pseudo-arc and the pseudo-solenoids) as Fraïssé limits. Our framework extends the discrete Fraïssé theory, both classical and projective, and is also suitable for working directly with continuous maps on metrizable compacta. We show, in particular, that, when playing with continuous surjections between non-degenerate Peano continua, the pseudo-arc is always generic. The universal pseudo-solenoid appears to be generic over all surjections between circle-like continua.
