تقرير
On homogeneous locally conical spaces
| العنوان: | On homogeneous locally conical spaces |
|---|---|
| المؤلفون: | Ancel, Fredric D., Bellamy, David P. |
| سنة النشر: | 2016 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - General Topology, Primary 54B15, 54F15, 54H99, Secondary 54H15, 57N15, 57S05 |
| الوصف: | The main result of this article is: THEOREM. Every homogeneous locally conical connected separable metric space that is not a $1$-manifold is strongly $n$-homogeneous for each $n \geq 2$ and countable dense homogeneous. Furthermore, countable dense homogeneity can be proven without assuming the space is connected. This theorem has the following two consequences. COROLLARY 1. If $X$ is a homogeneous compact suspension, then $X$ is an absolute suspension (i.e., for any two distinct points $p$ and $q$ of $X$, there is a homeomorphism from $X$ to a suspension that maps $p$ and $q$ to the suspension points). COROLLARY 2. If there exists a locally conical counterexample $X$ to the Bing-Borsuk Conjecture (i.e., $X$ is a locally conical homogeneous Euclidean neighborhood retract that is not a manifold), then $X$ is strongly $n$-homogeneous for all $n \geq 2$ and countable dense homogeneous. Comment: 14 pages, 5 figures. This is the final version of the paper that will appear in Fund. Math |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/1607.00103 |
| رقم الأكسشن: | edsarx.1607.00103 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |