Recent content by mairzydoats

I want to know if it can be shown using the topological definition of continuity instead of the beta epsilon way.

But to meet 2) you also have to show that there are open sets in the codomain whose preimages in the domain aren't open. Hence the question relating to preimages containing isolated points.

Edit above: "are disjoint unions of singletons?" --> "include and/or consist solely of isolated points?"

Preimages of open intervals are disjoint unions of singletons?

Do functions exist f: R --> R such that 1) f is an open map 2) f is noncontinuous, and 3) Both domain AND codomain are endowed with the usual topology? I'm aware of examples that satisfy 1) and 2) but which use the discreet topology on the codomain.

Are cartesian coordinates the only coordinates with a holonomic basis that's orthonormal everywhere?

Okay

When the cylinder is embedded, a secondary layer of bound densities is formed around it which oppose those of the P or M whose influence would otherwise be prevalent. That is why the method will measure H or D rather than E or B Too see what I mean you can try a thought experiment using my...

How so?

...which is model independent

...and so they are the usual assumptions for a good reason-they are the correct assumptions for the subject matter under discussion.

And besides, trying to discuss vector H on the quantum level doesn't even make any sense. H is defined as: H = B/μ° - M And M is by definition a macroscopic value. It is the magnetic dipole moment per unit volume. Undefined on the quantum level, and hence so too is H.

Yes, the usual assumptions in the macroscopic model.

The boundary condition which states that the discontinuity in the tangential component of the H at the border between two mediums is equal to the free surface current density J follows directly from the relation ∇ x H = Jfree + ∂D/∂t

But inside of a perfect conductor, there is no "polarization/magnetization" by definition. All charges/currents are "free charges/currents" and are at the surface. Where does choice come in? ...And what would you "shuffle" to change the conclusion you would be unavoidably directed to about...