On Raymond-Williams' example

TL;DR

This paper simplifies the construction of a p-adic integer action on an n-dimensional compact space, resulting in an orbit space of dimension n+2, extending Raymond and Williams' original example.

Contribution

It provides a more straightforward method to construct p-adic actions on compact spaces with specified orbit space dimensions.

Findings

Simplified construction of p-adic integer actions

Extended the known examples to higher dimensions

Clarified the relationship between actions and orbit space dimensions

Abstract

Raymond and Wiliams in "Examples of p-adic transformation groups", Ann. of Math. (2) 78 (1963) 92-106, constructed an action of the p-adic integers on an n-dimensional compactum, n>1, with the orbit space of dimension n+2. We present a simpler construction of such an example.