Peano Quotients of Metric Continua

For any compact, connected metric space $(M,d)$ the set of points where $M$ is not weakly locally connected is shown to define a partition $\text{sP}$ of $M$ for which the corresponding quotient metric space $(\text{sQ},{\mathrm{\nabla }}_{\text{sQ}})$ is a Peano continuum with $\text{sQ}=\text{sP}$.