Let $[0, 1]^{\mathbb N}$ be equipped with the box topology.

Asked Jul 22 '21 at 06:09

Active Jul 22 '21 at 06:09

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Let $X = [0, 1]^{\mathbb N}$ be equipped with the box topology. Prove or Disprove that

$[0, 1]^{\mathbb N}$ is connected.

From what I've known $[0, 1]^{\mathbb N}$ is not compact based on this answer. Now it bothers me if the latter is connected and how to show if it is or not.

asked Jul 22 '21 at 06:09

Dencio

This might help -- $[0,1]^\mathbb{N}$ is not a subset of any of the components, so it is not connected. – Amit Rajaraman Jul 22 '21 at 06:41
duplicate https://math.stackexchange.com/q/4205293 – Mirko Jul 23 '21 at 17:05

Let $[0, 1]^{\mathbb N}$ be equipped with the box topology.

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