| Autor: |
Krupski, Paweł, Samulewicz, Alicja |
| Rok vydání: |
2016 |
| Předmět: |
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| Zdroj: |
Topology and its Applications 221 (2017), 352-369 |
| Druh dokumentu: |
Working Paper |
| DOI: |
10.1016/j.topol.2017.02.055 |
| Popis: |
The family of all subcontinua that separate a compact connected $n$-manifold $X$ (with or without boundary), $n\ge 3$, is an $F_\sigma$-absorber in the hyperspace $C(X)$ of nonempty subcontinua of $X$. If $D_2(F_\sigma)$ is the small Borel class of spaces which are differences of two $\sigma$-compact sets, then the family of all $(n-1)$-dimensional continua that separate $X$ is a $D_2(F_\sigma)$-absorber in $C(X)$. The families of nondegenerate colocally connected or aposyndetic continua in $I^n$ and of at least two-dimensional or decomposable Kelley continua are $F_{\sigma\delta}$-absorbers in the hyperspace $C(I^n)$ for $n\ge 3$. The hyperspaces of all weakly infinite-dimensional continua and of $C$-continua of dimensions at least 2 in a compact connected Hilbert cube manifold $X$ are $\Pi ^1_1$-absorbers in $C(X)$. The family of all hereditarily infinite-dimensional compacta in the Hilbert cube $I^\omega$ is $\Pi ^1_1$-complete in $2^{I^\omega}$. |
| Databáze: |
arXiv |
| Externí odkaz: |
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