mathematics – Konrad Voelkel's Blog – Mathemagically

Is it possible to prove the Quillen-Suslin theorem analogous to the classical theorem on vector bundles over contractible spaces via representing the vectorbundle-up-to-iso-functor in the homotopy category by infinite Grassmannians?

A mind-map overview of the most important single variable complex analysis theorems and some implications between them (complex calculus, first course).

A closed immersion is finite. A finite morphism is proper, affine and of finite type. Finite morphisms are separated. Open immersions are etale, therefore smooth, thus flat; open immersions are separated. Quasi-compact and locally of finite type implies of finite type. Projective and quasi-finite is the same as finite. Proper morphisms are universally closed. Flat morphisms of finite type are universally open.

Definition of essential manifolds, lens spaces as example of non-aspherical essential manifolds.