On imbedding of closed 2-dimensional disks into $R^2$

dc.creatorPolulyakh, Eugene
dc.date1999-07-24
dc.date.accessioned2026-07-07T05:30:03Z
dc.date.available2026-07-07T05:30:03Z
dc.descriptionLet $X$ 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.descriptionLaTeX-2e document, 28 pages
dc.identifierhttps://arxiv.org/abs/math/9907162
dc.identifierhttp://arxiv.org/abs/math/9907162
dc.identifierMethods of Func. An. and Topology - 1998 - N 2 - P. 76-94
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/78874
dc.subjectGeometric Topology
dc.subjectAlgebraic Topology
dc.subject14E35; 57M50; 57N35
dc.titleOn imbedding of closed 2-dimensional disks into $R^2$
dc.typetext

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