1. Simplest counterexample about path connectedness

We know that path connectedness implies connectedness, but the converse doesn't hold.

What's the simplest counterexample?

2. I've seem comb space most frequently.

Comb space - Wikipedia, the free encyclopedia

3. Originally Posted by Connected
We know that path connectedness implies connectedness, but the converse doesn't hold.

What's the simplest counterexample?
Or the Topologist sign curve.