More non-analytic classes of continua
- 作者：Krupski ; Pawel
- 关键词：54H05 ; 54F15 ; 54F45 ; 03E15 ; Coanalytic set ; Coanalytic complete ; Chainable continuum ; Inverse limit ; Clump of continua ; λ ; -dendroid ; Tree-like continuum ; Pseudo-arc ; Pseudo-solenoid ; Countable-dimensional ; Weakly infinite-dimensional
- 刊名：Topology and its Applications
- 出版年：2003
- 期刊代码：60_01668641
- 类别：mt
- 出版时间：January 15, 2003
- 卷：127
- 期：3
- 页码：299-312
- 文件大小：126 K
摘要
The method of [U. Darji, Topology Appl. 103 (2000) 243–248] is extended to get the coanalytic hardness of many classes of metric continua. For instance: (1) the family of all continua in In, n≥2, that admit only arcs (simple closed curves) as chainable (circularly chainable) subcontinua is coanalytic complete; (2) the family of all continua in In, n≥2 (n≥3), which contain no copy of a given nondegenerate chainable (circularly chainable) continuum Y is coanalytic hard; if Y is an arc or a pseudo-arc (a simple closed curve or a pseudo-solenoid), then the family is coanalytic complete; (3) the family of all tree-like continua that contain no hereditarily decomposable subcontinua is coanalytic hard; (4) the family of all λ-dendroids that contain no arcs is coanalytic complete; (5) the sets of all countable-dimensional continua and of all weakly infinite-dimensional continua in the Hilbert cube are coanalytic hard; strongly countable-dimensional continua form a coanalytic complete family.