Topological manifold

The description of fuzzy, local density fragments is facilitated by the use of local coordinate systems, however, some compatibility conditions of such local coordinate systems must be fulfilled, reflecting the mutual relations of the fragments within the complete molecule. Manifold theory, topological manifolds, and in particular, differentiable manifolds [153-158], are the branches of mathematics dealing with the general properties of compatible local coordinate systems. 

Mezey, P.G., Reaction Topology Manifold Theory of Potential Surfaces and Quantum Chemical Synthesis Design, in Chemical Applications of Topology and Graph Theory, Elsevier Sci. 

A compact n-dimensional topological manifold M has the structure of a simple n-dimensional geometric Poincare complex. The intersection pairing of o (M)... 

The total surgery obstruction theory of Ranicki [7] was a tentative first step towards a purely algebraic account of the homotopy theory of compact n-dimensional topological manifolds, at least for n 5, including an algebraic expression for the surgery exact sequence. 

The (X, T) couple is called a topological space on X. If X is a metric space (endowed with a distance), the canonical topology is defined from the corresponding open balls of X (each of them being defined by a center and a radius). A topological space (X, T) is a topological manifold if it is separated and locally euclidean, i.e. every point in X admits an open neighborhood homeomorphic to M n is unique and defines the dimension of X, then referred to as a nD-manifold. 

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