Kelley continuum

A continuum $X$ is called a Kelley continuum if for every subcontinuum $K$ of $X$, for every point $p \in K$, and for every sequence $p_n\to p$ there are continua $K_n$ such that $p_n \in K_n $ and $K_n\to K$. Other names used: property (3.2), a property of Kelley, the property of Kelley, Kelley’s property, property $(\kappa)$.