C(X)中Whitney连续体的可缩性

General Topology and its Applications Pub Date : 1978-11-01 DOI:10.1016/0016-660X(78)90031-4

Ann Petrus

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引用次数: 27

摘要

我们证明了2-cell上存在Whitney映射，使得2-cell的超空间中的Whitney连续体是不可收缩的，非局部可收缩的，并且在2维空间中具有非平凡Čhech上同调。这意味着可收缩性、局部可收缩性、是AR、是ANR和Čech上同调中的不环性不是惠特尼性质。然而，我们证明了树突类的可收缩性是惠特尼性质。

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Contractibility of Whitney continua in C(X)

We show that there are Whitney maps on the 2-cell such that Whitney continua in the hyperspace of the 2-cell are non-contractible, non-locally contractible, and have non-trivial Čhech cohomology in dimension 2. This implies that contractibility, local contractibility, being an AR, being an ANR, and acyclicity in Čech cohomology are not Whitney properties. We show, however, that contractibility is a Whitney property for the class of dendrites.

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