On imbedding of closed 2-dimensional disks into $R^2$
| dc.creator | Polulyakh, Eugene | |
| dc.date | 1999-07-24 | |
| dc.date.accessioned | 2026-07-07T05:30:03Z | |
| dc.date.available | 2026-07-07T05:30:03Z | |
| dc.description | Let $X$ be a topological space, $U$ -- opened subset of $X$. We will say that point $x \in \partial U$ is {\it accessible} from $U$ if there exists continuous injective mapping $ϕ: I \to \Cl D$ such that $ϕ(1)=x$, $ϕ([0,1)) \subset \Int U$. We proove the next main theorem. The following conditions are neccesary and suffficient for a compact subset $D$ of $R^2$ with a nonempty interior $\Int D$ to be homeomorphic to a closed 2-dimensional disk: 1) sets $\Int D$ and $R^2 \setminus D$ are connected; 2) any $x \in \partial D$ is accessible both from $\Int D$ and from $R^2 \setminus D$. | |
| dc.description | LaTeX-2e document, 28 pages | |
| dc.identifier | https://arxiv.org/abs/math/9907162 | |
| dc.identifier | http://arxiv.org/abs/math/9907162 | |
| dc.identifier | Methods of Func. An. and Topology - 1998 - N 2 - P. 76-94 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/78874 | |
| dc.subject | Geometric Topology | |
| dc.subject | Algebraic Topology | |
| dc.subject | 14E35; 57M50; 57N35 | |
| dc.title | On imbedding of closed 2-dimensional disks into $R^2$ | |
| dc.type | text |