What is the horrible meaning of Klein bottle?

The horror of Klein bottle is that it has no "edge" and its surface will not end.

The structure of Klein bottle can be expressed as follows: there is a hole in the bottom of the bottle. Now the bottleneck is stretched out and screwed into the bottle, and then connected with the hole in the bottom of the bottle. Unlike the cup we usually use to drink water, this object has no "edge" and its surface will not end. It is different from a sphere. A fly can fly directly from the inside of the bottle to the outside without passing through the surface, that is, it has no distinction between inside and outside.

Behind the story:

1882, the famous mathematician Felix Klein discovered the famous "bottle" named after him later. This is a closed surface like a sphere (that is, there is no edge), but there is only one face.

In the picture, we can see that Klein bottle really looks like a bottle. But it doesn't have a bottle bottom, its bottleneck is elongated, then it seems to pass through the bottle wall, and finally the bottleneck is connected with the bottle bottom ring. If the bottleneck is connected to the bottom ring of the bottle from the other side without passing through the bottle wall, we will get a tire tread (that is, a torus).