  In this work we propose a new type of shift spaces, called blur shift spaces,
where one can represent with a single symbol an entire set of infinite symbols.
Such shift spaces are constructed from classical shift spaces, by choosing some
sets of infinitely many symbols that will be represented by a new symbol, and
then defining a convenient topology. The shift spaces we are proposing
generalize ideas presented previously by Ott, Tomforde and Willis, and by
Gon\c{c}alves and Royer, which were used to find isomorphism between
$C^*$-algebras associated to some classes of shift spaces. In particular, blur
shifts can be used as a compactification scheme for classical shift spaces.
