Let $X$ be a countable discrete topological space. Consider $X^{\mathbb{N}}$ endowed with the product topology.
How do you prove that $X^{\mathbb{N}}$ is homeomorphic to the sub-space of all irrational numbers?
Let $X$ be a countable discrete topological space. Consider $X^{\mathbb{N}}$ endowed with the product topology.
How do you prove that $X^{\mathbb{N}}$ is homeomorphic to the sub-space of all irrational numbers?