The Cambridge Colloquium 1916, Vol. 2: Analysis Situs (Classic Reprint) - Hardcover

Inhaltsangabe

Excerpt from The Cambridge Colloquium 1916, Vol. 2: Analysis Situs

It will be seen that, aside from this one question which has to be dealt with in order to give significance to the combinatorial treatment, we leave out of consideration all the work that has been done on the point-set problems of Analysis Situs and on its foundation in terms of axioms or definitions other than those actually used in the text. We have also been obliged by lack of space to leave out all reference to the applications. We have not even given a definition of an n - cell by means of a set of equa tions and inequalities, or the discussion of orientation by means of the signs of determinants. These are to be found in very readable form in Poincaré's first paper, where they are given as the basis of his work. They belong properly, however, to the applications of the subject. For in nearly all cases when Poincaré (or anyone else) has proved a theorem of Analysis Situs, he has been obliged to set up a machinery which is equivalent to a set of matrices.

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