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Could this non-Hausdorff world with two skies be logically coherent?

Original post on worldbuilding.stackexchange by Ichthys King

Dicaelus is a strange world. It is flat, with a deep sea covering the world. Above this sea are endless archipelagos of floating islands

The strange part is that the vertical axis is not a regular axis, but is instead a branching line. This is where there are two lines that are identified on only one side of the origin. The origin in this world is between the islands and the sea, with one sea and two distinct skies and sets of islands. Objects can cross the origin from either sky to the sea, or from the sea into either sky

Given the strange nature of this place, could such a world logically exist?

Answer by elemtilas

Yes.

This makes perfect sense.

This logically exists in the real world. All you have to do is, for example, put your kid in front in front of you and see in her face every day of her life from the spark of her first origin to the moment of her last breath. Not as a linear movie with distinct images, but as polytemporal snapshot.

The world you’re describing is similar only with solid polyphysicality rather than iconic polytemporality.

Think about it, perhaps, like this:

Plant a tree with a Y shaped trunk. Train the upper part of the wye to converge. Once the two upper trunks are dually parallel, bind them until the two Y trunk looks like an I trunk.

The unified trunk down by the ground is the Sea. The two skies are the bound Y trunks up above.

If you could place a very tiny exploratory vehicle inside one of the upper trunks, you’d be able to drive it up and down either side of the wye, but you couldn’t cross between one and the other.

From the outside, all the leaves — the islands of the two skies — look like a single tangle of leaves.

The reason why this description fails, of course, is because of the limitations of our local geometry. What you would end up with is someone who lives on an island in Bluesky, can’t see or interact with someone who lives on an island in Greensky, where logically both are in the same place.

Bluesky girl has to descend towards the Sea where she can see both Bluesky and Greensky coexisting in the same place. Thence she must ascend through Greensky to visit her friend who literally lives in the same exact place, only under a different sky.