solidot新版网站常见问题,请点击这里查看。
消息
本文已被查看3938次
A Core Decomposition of Compact Sets in the Plane. (arXiv:1712.06300v1 [math.DS])
来源于:arXiv
A compact metric space is called a \emph{generalized Peano space} if all its
components are locally connected and if for any constant $C>0$ all but finitely
many of the components are of diameter less than $C$. Given a compact set
$K\subset\mathbb{C}$, there usually exist several upper semi-continuous
decompositions of $K$ into subcontinua such that the quotient space, equipped
with the quotient topology, is a generalized Peano space. We show that one of
these decompositions is finer than all the others and call it the \emph{core
decomposition of $K$ with Peano quotient}. For specific choices of $K$, this
core decomposition coincides with two models obtained recently, namely the
locally connected models for unshielded planar continua (like connected Julia
sets of polynomials) and the finitely Suslinian models for unshielded planar
compact sets (like disconnected Julia sets of polynomials). We further answer
several questions posed by Curry in 2010. In particular, we can exclude the 查看全文>>