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

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

1999-07-24

arxiv.org/abs/math/9907162v1

Methods of Func. An. and Topology - 1998 - N 2 - P. 76-94

Mathematics

Geometric Topology

LaTeX-2e document, 28 pages

Scientific paper

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 $\phi : I \to \Cl D$ such that $\phi(1)=x$, $\phi([0,1)) \subset \Int U$. 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 $R^2 \setminus D$.

Affiliated with

Also associated with

No associations

Rating

On imbedding of closed 2-dimensional disks into $R^2$ does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On imbedding of closed 2-dimensional disks into $R^2$, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On imbedding of closed 2-dimensional disks into $R^2$ will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-185214