Area of Geometry and Topology

In this paper, we give a method to construct a zero-dimensional Wallman compactication for a zero-dimensional T0 space. This allows us to give new proofs of the following results: every T0 zero-dimensional space is a Tychono space, C (the Cantor set) is universal for the class of zero-dimensional separable metrizable spaces and Q is the only countable perfect metrizable space ( rst proved by Sierpinski in 1920). Key words and phrases: Wallman compactication, zero-dimensio-nal, Cantor set, universal space, rational numbers