This is related to the example of @AndreasBlass.

If $A$ is some finite set, then consider the space of all infinite sequences $A^{\mathbb N}$ with the product topology. Then certain sets of infinite sequences, called recognizable, could be described by Büchi automata. A recognizable set is a $G_{\delta}$-set if and only if it could be described by a deterministic Büchi automaton.

This is related to the example of @AndreasBlass.

If $A$ is some finite set, then consider the space of all infinite sequences $A^{\mathbb N}$ with the product topology. Then certain sets of infinite sequences, called recognizable, could be described by Büchi automata. A recognizable set is a $G_{\delta}$-set if and only if it could be described by a deterministic Büchi automaton.

This is related to the example of @AndreasBlass.

If $A$ is some finite set, then consider the space of all infinite sequences $A^{\mathbb N}$ with the product topology. Then certain sets of infinite sequences, called recognizable, could be described by Büchi automata. A recognizable set is a $G_{\delta}$-set if and only if it could be described by a deterministic Büchi automaton.

This is related to the example of @AndreasBlass.

If $A$ is some finite set, then consider the space of all infinite sequences $A^{\mathbb N}$ with the product topology. Then certain sets of infinite sequences, called recognizable, could be described by Büchi automata. A recognizable set is a $G_{\delta}$-set if and only if it could be described by a deterministic Büchi automaton.