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 $K\subset\hat{\bbC}$, including a gluing lemma for lambda functions and some inequalities... (read more)

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