cianfa72's latest activity

Let me try to recap my understanding about this. In the context of category theory, given two objects ##X_1## and ##X_2## of a given...

It seems indeed this is the usual meaning of trivial, i.e. equivalent to a product, but without a choice of trivialization. I was...

As far as I can understand, your point is that a trivial bundle includes two pieces of information: a trivializable bundle plus a...

You mean, take a topological space ##B## that is homeomorphic to the Cartesian product ##A \times F##. The choice of the homeomorphism...

A choice of a product decomposition of a topological space that is homeomorphic to a Cartesian product AxF naturally supplies a...

Yes, but for the case of product bundle the projection mapping is canonically/naturally given by the structure of the product (it is one...

Though I don't think this is an approximation, but rather bending the rules to make things simpler. The following is from Morin Once...

Ok, you are assuming the inertial rest frame of the table. By Newton 3rd law, the book acts with a force on the table, so there must be...

You mean the table doesn't move w.r.t. the rest frame of "book + table" system's Center-of-Mass.

Yes, for instance in the rest frame of the "Earth + object" system's Center-of-Mass, the kinetic energy is basically associated to the...

Sure, but note that mechanical energy is the sum of kinetic plus potential energy. Therefore, in my expression, it is implied that...

I'd like to point out that the increase in mechanical energy associated with lifting an object up, goes into the potential energy of the...

Not really, because you don't have a sense of "location" without defining "at rest", and you are again using "in a reference frame"...

Nothing can leave the future light cone of any event on its past worldline, would be the formal statement that generalises to curved...

Note that this centripetal force (inward proper acceleration) is given by the spring acting on the mass (not the other way around). The...