Classical Swiss Cheese Sets

Abstract Swiss Cheese Space and the Classicalisation of Swiss Cheeses

We introduce a topological space whose elements are what we call"abstract swisscheeses".We first give a new proof of the feinstein-heath classicalisation theorem.We then consider when it is possible to"classicalise"a swiss cheese while leaving disks which lie outside a given region unchanged.We also consider setsobtained by deleting a sequence of open disks from a closed annulus, and we obtain an analogue of the feinstein-heath theorem for these sets.We then discuss regularity for certain uniform algebras.