pi-base
Lexicographical $[0,1]^\omega$: A space that is LOTS+connected+totally path disconnected
Two years ago I got from https://math.stackexchange.com/questions/4453285 that $[0,1]^\omega$ is a nontrivial example for a LOTS that is connected and totally path disconnected (such example does not exist in $\pi$-base up to now).
How would you name this space? Does "Lexicographical Hilbert cube" sounds good?
@Jianing-Song (Unrelated to this issue) If you have the chance, could you take a look at https://math.stackexchange.com/questions/4913495/every-second-countable-lots-is-embeddable-in-mathbb-r? I will add this to pi-base after it gets validated.
@Jianing-Song (Unrelated to this issue) If you have the chance, could you take a look at https://math.stackexchange.com/questions/4913495/every-second-countable-lots-is-embeddable-in-mathbb-r? I will add this to pi-base after it gets validated.
Looks good to me :)