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https://en.wikipedia.org/wiki/Surface_(topology)#Classification_of_closed_surfaces

Classification of closed surfaces[edit]Some examples of orientable closed surfaces (left) and surfaces with boundary (right). Left: Some orientable closed surfaces are the surface of a sphere, the surface of a torus, and the surface of a cube. (The cube and the sphere are topologically equivalent to each other.) Right: Some surfaces with boundary are the disk surface, square surface, and hemisphere surface. The boundaries are shown in red. All three of these are topologically equivalent to each other.The classification theorem of closed surfaces states that any connected closed surface is homeomorphic to some member of one of these three families:the sphere;the connected sum of g tori, for {\displaystyle g\geq 1} g\geq 1;the connected sum of k real projective planes, for {\displaystyle k\geq 1} k\geq 1.The surfaces in the first two families are orientable. It is convenient to combine the two families by regarding the sphere as the connected sum of 0 tori. The number g of tori involved is called the genus of the surface. The sphere and the torus have Euler characteristics 2 and 0, respectively, and in general the Euler characteristic of the connected sum of g tori is 2 − 2g.The surfaces in the third family are nonorientable. The Euler characteristic of the real projective plane is 1, and in general the Euler characteristic of the connected sum of k of them is 2 − k.It follows that a closed surface is determined, up to homeomorphism, by two pieces of information: its Euler characteristic, and whether it is orientable or not. In other words, Euler characteristic and orientability completely classify closed surfaces up to homeomorphism.Closed surfaces with multiple connected components are classified by the class of each of their connected components, and thus one generally assumes that the surface is connected.

closed surface...What had that even suppose to mean? In English?

So I am not talking about an ether that allows the electromagnetic field to traverse through, but an ether that allows carrier signals to traverse through.

So without the earths electromagnetic field the satellites would not work?

The carrier signal is also an electromagnetic wave. And there is no ether.

A satellite around Alpha Centauri would be able to work quite well (and communicate quite well) without Earth’s electromagnetic field

A closed surface is The Box. You know, The Box you put stuff in.Boxes come in all shapes - you can have regular shapes like cubes, dodecahedrons and spheres, or irregular shapes like an amoeba. Boxes come in all sizes - you can have small ones that are just big enough to hold an atom, and larger ones that can hold a star. The Box does not need to be a physical box, but it can also be a geometrical shape drawn in space. It is any box that has an inside and an outside.

could you give me any examples of what Maxwell's maths is used for in everyday use?

How can anyone write an equation without properly understanding what they are writing the equation for?

That is the beauty of theoretical physics.

Go to page 14 and look at figure 1.8. Let me know when you have done that.

PS: how can your equation have two “=0”?

"Space-time earth's" magnetic (field?)Space holds the energy, time provides a field for dimensions and earth as just a point of reference. So what earth has to do with the magnetic or the field at all?

Quote from: Alex Dullius Siqueira on 13/02/2018 22:30:27"Space-time earth's" magnetic (field?)Space holds the energy, time provides a field for dimensions and earth as just a point of reference. So what earth has to do with the magnetic or the field at all?All atoms have a field.

My question on the last years is: Do they? or it's the environment that does?

Quote from: Thebox on 14/02/2018 11:57:29Quote from: Alex Dullius Siqueira on 13/02/2018 22:30:27"Space-time earth's" magnetic (field?)Space holds the energy, time provides a field for dimensions and earth as just a point of reference. So what earth has to do with the magnetic or the field at all?All atoms have a field. : Do they? or it's the environment that does?