تقرير
Hyperspaces of countable compacta
| العنوان: | Hyperspaces of countable compacta |
|---|---|
| المؤلفون: | Banakh, Taras, Krupski, Paweł, Omiljanowski, Krzysztof |
| سنة النشر: | 2019 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - General Topology, 57N20, 54B20, 54H05 |
| الوصف: | Hyperspaces $\mathcal H(X)$ of all countable compact subsets of a metric space $X$ and $\mathcal A_n(X)$ of infinite compact subsets which have at most $n$ ($n\in\mathbb N$), or finitely many ($n=\omega$) or countably many ($n=\omega+1$) accumulation points are studied. By descriptive set-theoretical methods, we fully characterize them for 0-dimensional, dense-in-itself, Polish spaces and partially for $\sigma$-compact spaces $X$. Using the theory of absorbing sets, we get characterizations of $\mathcal H(X)$, $\mathcal A_\omega(X)$ and $\mathcal A_{\omega+1}(X)$ for nondegenerate connected, locally connected Polish spaces $X$ which are either locally compact or nowhere locally compact. For every $n\in\mathbb N$, we show that if $X$ is an interval or a simple closed curve, $\mathcal A_n(X)$ is homeomorphic to the linear space $c_{0}=\{(x_{i}) \in\mathbb R^{\omega}: \lim x_{i}=0\}$ with the product topology; if $X$ is a Peano continuum and a point $p\in X$ is of order $\ge 2$, then the hyperspace $\mathcal A_1(X,\{p\})$ of all compacta with exactly one accumulation point $p$ also is homeomorphic to $c_{0}$. Comment: 28 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/1908.02845 |
| رقم الأكسشن: | edsarx.1908.02845 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |