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Lexicographical $[0,1]^\omega$: A space that is LOTS+connected+totally path disconnected #642

Open Jianing-Song opened 2 months ago

Jianing-Song commented 2 months ago

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?

prabau commented 2 months ago

Sounds like a great name.

prabau commented 2 months ago

@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 commented 2 months ago

@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 :)