In the late 90s Farah formulated the weak Extension Principle (wEP) for Čech--Stone remainders of zero-dimensional topological spaces. In a nutshell, the wEP asks to completely understand continuous functions between such Čech--Stone remainders. While this principle does not follow from the usual ZFC Axioms, being false for example under the Continuum Hypothesis, Farah showed some instances of wEP are a consequence of fairly mild axioms such as the Open Colouring Axiom and Martin's Axiom.

We explore generalisations of the wEP to all Čech--Stone remainders of locally compact metrizable spaces, and state a coarse geometric version of wEP allowing to obtain (again under reasonable set theoretic assumptions) rigidity results for Higson coronas, boundary spaces arising in coarse geometry.