# Search results

1. ### I Which class of functions does 1/x belong to?

Well, of course, but I meant its classification from the viewpoint of functional analysis.

Thank you!
3. ### I Which class of functions does 1/x belong to?

I am not sure I understand your point. The analytic functions form a small and restrictive class of functions. It can be broadened by dropping some requirements imposed on class members. It gives us this sequence (incomplete, I guess, but it illustrates the basic idea): ##C^\omega \subset...
4. ### I Which class of functions does 1/x belong to?

Yes, you are right. I was thinking about interval [-1,1].
5. ### I Which class of functions does 1/x belong to?

For historical reasons the hyperbola always was considered to be one of the «classical» curves. The function, obviously, does not belong to C0. Apparently, is does not fit L2 or any other Lp? What is the smallest class?
6. ### A Concept of duality for projective spaces and manifolds

Thank you for such a thorough explanation. The whole picture clarified considerably. But one point still escapes me. Let's say we have a differentiable (smooth) manifold. It «generates» tangent and co-tangent linear (vector!) spaces, that are dual to each other. The question is whether those...
7. ### A Concept of duality for projective spaces and manifolds

It looks like we are sailing on parallel courses here. I received no special education in mathematics and sincerely believed projective geometry to be some set of formal rules used in doing technical or architecture drawing, something that albeit being practicallly important just thrives on...
8. ### A Concept of duality for projective spaces and manifolds

Yes, you are right! Metric tensor mapping vectors to one-forms can be visualised as a circle in Euclidean space (I read about this in «Spacetime, geometry, cosmology» by W. L. Burke). The way to recover one-form from vector (arrow) and tensor (circle) is the same procedure as construction of...
9. ### A Concept of duality for projective spaces and manifolds

I firstly learned about duality in context of differentiable manifolds. Here, we have tangent vectors populating the tangent space and differential forms in its co-tangent counterpart. Acting upon each other a vector and a form produce a scalar (contraction operation). Later, I run into the...
10. ### A Why are conics indistinguishable in projective geometry?

Thank you for pointing (projecting :-)) me in the right direction. I have found the book you recommended and I like it much. Exactly kind of book I needed. Join to Micromass in sincere recommending this book to everyone who is looking for elucidation for subjects like the one discussed in this...
11. ### A Why are conics indistinguishable in projective geometry?

It is said that curves of the second order which we usually refer to as ellipse, parabola and hyperbola, i. e. conics, are all represented on projective plane by closed curves (oval curve), which means there is no distinction between them. Why is it? Projective space can, in principle, be...