A full shift over a finite alphabet 
is the set 
of all bi-infinite sequences
of symbols from 
,
equipped with the left shift
 |
where 
ranges over the integers
(Lind and Marcus 2021, pp. 1-3). The alphabet has
the discrete topology, and 
has the corresponding product
topology (Kůrka 2009).
For a positive integer 
, the full 
-shift uses the alphabet 
. It places no restrictions
on which symbols can follow one another. Replacing the index
set 
by the nonnegative integers gives the one-sided
full shift. A shift space is a shift-invariant closed subset of a full shift, possibly the full shift
itself.
