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- W4303093510 abstract "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." @default.
- W4303093510 created "2022-10-07" @default.
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- W4303093510 date "2016-06-30" @default.
- W4303093510 modified "2023-10-16" @default.
- W4303093510 title "On homogeneous locally conical spaces" @default.
- W4303093510 doi "https://doi.org/10.48550/arxiv.1607.00103" @default.
- W4303093510 hasPublicationYear "2016" @default.
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