I'm not sure what the author has in mind, but a standard way to put a topology on this space would be to use the discrete topology [1] on {0, 1}, and then use t

I'm not sure what the author has in mind, but a standard way to put a topology on this space would be to use the discrete topology [1] on {0, 1}, and then use the product topology [2] to obtain a topology over the space of binary streams. This space is homeomorphic to the Cantor set (see "Examples" section in [2]), so you can think of it as being the same topology as the Cantor set. [1] https://en.wikipedia.org/wiki/Discrete_space https://en.wikipedia.org/wiki/Discrete_space [2] https://en.wikipedia.org/wiki/Product_topology https://en.wikipedia.org/wiki/Product_topology