Recognizing indecomposable subcontinua of surfaces from their complements

Details Recognizing indecomposable subcontinua of surfaces from their complements Recognizing indecomposable subcontinua of surfaces from their complements

2008-06-25

arxiv.org/abs/0806.4009v1

Topology Proc. 33 (2009), 251--268

Mathematics

General Topology

14 pages

Scientific paper

We prove two theorems which allow one to recognize indecomposable subcontinua of closed surfaces without boundary. If $X$ is a subcontinuum of a closed surface $S$, we call the components of $S \setminus X$ the complementary domains of $X$. We prove that a continuum is either indecomposable or the union of two indecomposable continua whenever it has a sequence of distinct complementary domains whose boundaries limit to the continuum in the Hausdorff metric. We define a slightly stronger condition on the complementary domains of a continuum, called the double-pass condition, which we conjecture is equivalent to indecomposability of the continuum. We prove that this is so for continua which are not the boundary of one of their complementary domains.

Affiliated with

Also associated with

No associations

Rating

Recognizing indecomposable subcontinua of surfaces from their complements 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 Recognizing indecomposable subcontinua of surfaces from their complements, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Recognizing indecomposable subcontinua of surfaces from their complements will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-162266