If the sea line is an arc with high in the middle and low on the left and right ends it will not close around.It's a simple fact.
If the sea line is a straight line and the sea surface is a sphere.The sea line will close in a circle.
What you really mean by "sea line"? The horizon? If yes, it is not a line. A line is something that connects two points, and it is straight, if not it will be a "curve".
So, rephrasing your first sentence, "If the sea curve is an arc, with high in the middle and low on the sides, it will not close around, It's a simple fact".... and NO, it can close on the bottom. An arc can be part of a round circle or ellipsoid closed object. Why you say it can not close around? as a fact... ? That is what nobody is understanding. What you mean by that? By any chance are you saying it will not "close around horizontally"? If yes, you need to put more words in the text, so we don't get confused.
Your second sentence makes no sense at all. "If the sea line(?) is straight and the sea surface is a sphere, the sea line(?) will close in a circle".
Again, this is a very difficult (for me) to understand what you mean by "sea line". What you mean by "sea line is straight"?
The sea surface is not a sphere, never is. A sphere represents a globe, the Earth's oceans do not make a globe, they are over a globe, the patches of land above the water makes it not a spherical water. Think with me, when you submerge an orange under water, still a spherical orange, even when you remove from water and it still all wet, still a spherical orange. The water could be covering a spherical orange, spherical planet and ultimate copying its format, but it is not a sphere.
Rethink and rephrase, mostly about the "sea line".