Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, and especially topology, a pseudomanifold is a special type of topological space. A topological space X endowed with a triangulation K is an n-dimensional pseudomanifold if the following conditions hold: 1. X = |K| is the union of all n-simplices. 2. Every (n – 1)-simplex is a face of exactly two n-simplices. 3. For every pair of n-simplices and ' in K, there is a sequence of n-simplices = 0, 1, …, k = ' such that the intersection i i+1 is an (n – 1)-simplex for all i. A pseudomanifold can be considered as a combinatorial realisation of the general idea of a manifold with singularities. The concepts of orientability, orientation and degree of a mapping make sense for pseudomanifolds and moreover, within the combinatorial approach, pseudomanifolds form the natural domain of definition for these concepts.

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