 It may be given the structure of a topological space according to the Cantor topology, in which the fundamental open sets are the sets of configurations that match any single pattern and the open sets are arbitrary unions of fundamental open sets.In this topology, a function from configurations to configurations is continuous if, for any fixed pattern defining a fundamental open set , the set of configurations mapped by into can itself be described by a (possibly infinite) set of patterns, with the property that a configuration belongs to if and only if it matches a pattern in .The shift map is a particular continuous function on the shift space that transforms a configuration into a new configuration in which each symbol is shifted one position over from its previous position