Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Lambda Function and a Quantification of Torhorst Theorem   To any compact $K\subset\hat{\mathbb{C}}$ we associate a map $\lambda_K:
\hat{\mathbb{C}}\rightarrow\mathbb{N}\cup\{\infty\}$ -- the lambda function of
$K$ -- such that a planar continuum $K$ is locally connected if and only if
$\Lambda_K(x)\equiv0$. We establish basic methods of determining the lambda
function $\lambda_K$ for specific compacta $K\subset\hat{\mathbb{C}}$,
including a gluing lemma for lambda functions and some inequalities. One of
these inequalities comes from an interplay between the topological difficulty
of a planar compactum $K$ and that of a sub-compactum $L\subset K$, lying on
the boundary of a component of $\hat{\mathbb{C}}\setminus K$. It generalizes
and quantifies the result of Torhorst Theorem, a fundamental result from plane
topology. We also find three conditions under which this inequality is actually
an equality. Under one of these conditions, this equality provides a
quantitative version for Whyburn's Theorem, which is a partial converse to
Torhorst Theorem.

19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex