Topological Foundations for a Formal Theory of Manifolds

Topological manifolds form an important class of topological spaces with applications throughout mathematics. However, the development of this scienti c area, even at the initial stage, requires non-trivial Brouwer's theorems: the xed point theorem, the topological invariance of degree, and the topological invariance of dimension, where each of them is provided for n-dimensional case. We present a formalization, that is checked in the Mizar system, of several results in algebraic topology that is su cient to show the basic properties of manifolds with boundary of dimension n.