In this talk we shall present generalizations of the Curtis-Hedlund-Lyndon Theorem for sliding block codes between shift spaces over infinitely countable alphabets. More specifically, we will consider non-compact shift spaces (with the product topology) and compacted shift spaces (with the Ott-Tomforde-Willis topology).

First we will give a new definition for sliding block codes, which is equivalent to the usual definition whenever the shift spaces have finite alphabet. Then, we will discuss the consequences of consider such definition for the case of shift spaces defined over infinitely countable alphabets.

This work was supported by CNPq-Brazil grants.