Displaying similar documents to “Smooth structures on Pi-manifolds”

Brouwer Invariance of Domain Theorem

Karol Pąk (2014)

Formalized Mathematics

Similarity:

In this article we focus on a special case of the Brouwer invariance of domain theorem. Let us A, B be a subsets of εn, and f : A → B be a homeomorphic. We prove that, if A is closed then f transform the boundary of A to the boundary of B; and if B is closed then f transform the interior of A to the interior of B. These two cases are sufficient to prove the topological invariance of dimension, which is used to prove basic properties of the n-dimensional manifolds, and also to prove basic...

An intrinsic definition of the Colombeau generalized functions

Jiří Jelínek (1999)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

A slight modification of the definition of the Colombeau generalized functions allows to have a canonical embedding of the space of the distributions into the space of the generalized functions on a 𝒞 manifold. The previous attempt in [5] is corrected, several equivalent definitions are presented.