An Arithmetic Treatment of Some Problems in Analysis Situs: A Dissertation Submitted to the Faculty of Arts and Sciences of Harvard University in ... of Doctor of Philosophy (Classic Reprint) - Softcover
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Excerpt from An Arithmetic Treatment of Some Problems in Analysis Situs: A Dissertation Submitted to the Faculty of Arts and Sciences of Harvard University in Satisfaction of the Requirement of a Thesis for the Degree of Doctor of Philosophy
More recently oh.-j. De la Valleé Poussin has published an outline of a proof of the same theorem for the most general simple curve. This work appears much more simple than either of the proofs already mentioned, but it is not arithmetic in form, and it is not easy to see how the arithmetization is to be effected. It can, therefore, be regarded only as a sketch of whatever rigorous proof may be made following its lines.
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An Arithmetic Treatment of Some Problems in Analysis Situs (Classic Reprint)
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Paperback. Condition: New. Print on Demand. This book presents an arithmetic treatment of some problems in analysis situs, which is the study of the properties of geometric objects that are invariant under continuous transformations. A problem in this field that had yet to be solved was the question of whether a closed curve in two-dimensional space divides the plane into an interior and an exterior region. The author introduces a set of axioms and arithmetic principles for analysis situs and proceeds to prove the theorem that a simple closed curve divides the plane into two regions, an interior, and an exterior. Next, the author extends this theorem to three-dimensional space, proving that a simple closed surface divides space into two regions, an interior and an exterior. The book concludes with a discussion of unilateral and bilateral surfaces, and the orientation of surfaces. It also provides the basis for extending the work to more than three dimensions. Anyone interested in analysis situs will find this a stimulating and thought-provoking work. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Seller Inventory # 9781334023941_0
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An Arithmetic Treatment of Some Problems in Analysis Situs A Dissertation Submitted to the Faculty of Arts and Sciences of Harvard University in of Doctor of Philosophy Classic Reprint
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An Arithmetic Treatment of Some Problems in Analysis Situs A Dissertation Submitted to the Faculty of Arts and Sciences of Harvard University in of Doctor of Philosophy Classic Reprint
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