Hausdorff On Ordered Sets
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Hausdorff On Ordered Sets
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Author : Felix Hausdorff
language : en
Publisher: American Mathematical Soc.
Release Date : 2005
Hausdorff On Ordered Sets written by Felix Hausdorff and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
Georg Cantor, the founder of set theory, published his last paper on sets in 1897. In 1900, David Hilbert made Cantor's Continuum Problem and the challenge of well-ordering the real numbers the first problem of his famous lecture at the international congress in Paris. Thus, as the nineteenth century came to a close and the twentieth century began, Cantor's work was finally receiving its due and Hilbert had made one of Cantor's most important conjectures his number one problem. It was time for the second generation of Cantorians to emerge. Foremost among this group were Ernst Zermelo and Felix Hausdorff. Zermelo isolated the Choice Principle, proved that every set could be well-ordered, and axiomatized the concept of set. He became the father of abstract set theory. Hausdorff eschewed foundations and developed set theory as a branch of mathematics worthy of study in its own right, capable of supporting both general topology and measure theory. He is recognized as the era's leading Cantorian. Hausdorff published seven articles in set theory during the period 1901-1909, mostly about ordered sets. This volume contains translations of these papers with accompanying introductory essays. They are highly accessible, historically significant works, important not only for set theory, but also for model theory, analysis and algebra. This book is suitable for graduate students and researchers interested in set theory and the history of mathematics. Also available from the AMS by Felix Hausdorff are the classic work, Grundzuge der Mengenlehre, and its English translation, Set Theory, as Volume 69 and Volume 119 in the AMS Chelsea Publishing series. Information for our distributors: Copublished with the London Mathematical Society. Members of the LMS may order directly from the AMS at the AMS member price. The LMS is registered with the Charity Commissioners.
Hausdorff On Ordered Sets
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Author : Felix Hausdorff
language : en
Publisher: American Mathematical Soc.
Release Date :
Hausdorff On Ordered Sets written by Felix Hausdorff and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
Georg Cantor, the founder of set theory, published his last paper on sets in 1897. In 1900, David Hilbert made Cantor's Continuum Problem and the challenge of well-ordering the real numbers the first problem of his famous lecture at the international congress in Paris. Thus, as the nineteenth century came to a close and the twentieth century began, Cantor's work was finally receiving its due and Hilbert had made one of Cantor's most important conjectures his number one problem. It was time for the second generation of Cantorians to emerge. Foremost among this group were Ernst Zermelo and Felix Hausdorff. Zermelo isolated the Choice Principle, proved that every set could be well-ordered, and axiomatized the concept of set. He became the father of abstract set theory. Hausdorff eschewed foundations and developed set theory as a branch of mathematics worthy of study in its own right, capable of supporting both general topology and measure theory. He is recognized as the era's leading Cantorian. Hausdorff published seven articles in set theory during the period 1901-1909, mostly about ordered sets. This volume contains translations of these papers with accompanying introductory essays. They are highly accessible, historically significant works, important not only for set theory, but also for model theory, analysis and algebra. This book is suitable for graduate students and researchers interested in set theory and the history of mathematics. Also available from the AMS by Felix Hausdorff are the classic work, Grundzuge der Mengenlehre, and its English translation, Set Theory, as Volume 69 and Volume 119 in the AMS Chelsea Publishing series. Information for our distributors: Copublished with the London Mathematical Society. Members of the LMS may order directly from the AMS at the AMS member price. The LMS is registered with the Charity Commissioners.
Set Theory
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Author : Felix Hausdorff
language : en
Publisher: American Mathematical Soc.
Release Date : 2005
Set Theory written by Felix Hausdorff and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
In the early twentieth century, Hausdorff developed an axiomatic approach to topology, which continues to be the foundation of modern topology. The present book, the English translation of the third edition of Hausdorff's Mengenlehre, is a thorough introduction to his theory of point-set topology. The treatment begins with topics in the foundations of mathematics, including the basics of abstract set theory, sums and products of sets, cardinal and ordinal numbers, and Hausdorff's well-ordering theorem. The exposition then specializes to point sets, where major topics such as Borel systems, first and second category, and connectedness are considered in detail. Next, mappings between spaces are introduced. This leads naturally to a discussion of topological spaces and continuous mappings between them. Finally, the theory is applied to the study of real functions and their properties. The book does not presuppose any mathematical knowledge beyond calculus, but it does require a certain maturity in abstract reasoning; qualified college seniors and first-year graduate students should have no difficulty in making the material their own.
Felix Hausdorff
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Author : Egbert Brieskorn
language : en
Publisher: Springer Nature
Release Date : 2024
Felix Hausdorff written by Egbert Brieskorn and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024 with Mathematicians categories.
Zusammenfassung: Felix Hausdorff is a singular phenomenon in the history of science. As a mathematician, he played a major role in shaping the development of modern mathematics in the 20th century. He founded general topology as an independent mathematical discipline, while enriching set theory with a number of fundamental concepts and results. His general approach to measure and dimension led to profound developments in numerous mathematical disciplines, and today Hausdorff dimension plays a central role in fractal theory with its many fascinating applications by means of computer graphics. Hausdorff 's remarkable mathematical versatility is reflected in his published work: today, no fewer than thirteen concepts, theorems and procedures carry his name. Yet he was not only a creative mathematician - Hausdorff was also an original philosophical thinker, a poet, essayist and man of letters. Under the pseudonym Paul Mongré, he published a volume of aphorisms, an epistemological study, a book of poetry, an oft-performed play, and a number of notable essays in leading literary journals. As a Jew, Felix Hausdorff was increasingly persecuted and humiliated under the National Socialist dictatorship. When deportation to a concentration camp was imminent, he, along with his wife and sister-in law, decided to take their own lives. This book will be of interest to historians and mathematicians already fascinated by the rich life of Felix Hausdorff, as well as to those readers who wish to immerse themselves in the intricate web of intellectual and political transformations during this pivotal period in European history
Ordered Sets
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Author : Egbert Harzheim
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-07-25
Ordered Sets written by Egbert Harzheim and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-07-25 with Mathematics categories.
This detailed textbook presents a great deal of material on ordered sets not previously published in the still rather limited textbook literature. It should be suitable as a text for a course on order theory.
Ordered Sets
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Author : Bernd Siegfried Walter Schröder
language : en
Publisher: Birkhauser
Release Date : 2003
Ordered Sets written by Bernd Siegfried Walter Schröder and has been published by Birkhauser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
A General Character Theory For Partially Ordered Sets And Lattices
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Author : Karl Heinrich Hofmann
language : en
Publisher: American Mathematical Soc.
Release Date : 1972
A General Character Theory For Partially Ordered Sets And Lattices written by Karl Heinrich Hofmann and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972 with Categories (Mathematics). categories.
Paradoxes Of Measures And Dimensions Originating In Felix Hausdorff S Ideas
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Author : Janusz Czyz
language : en
Publisher: World Scientific
Release Date : 1994-01-14
Paradoxes Of Measures And Dimensions Originating In Felix Hausdorff S Ideas written by Janusz Czyz and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-01-14 with Mathematics categories.
In this book, many ideas by Felix Hausdorff are described and contemporary mathematical theories stemming from them are sketched.
Fundamentals Of Set And Number Theory
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Author : Valeriy K. Zakharov
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2018-02-05
Fundamentals Of Set And Number Theory written by Valeriy K. Zakharov and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-05 with Mathematics categories.
This comprehensive two-volume work is devoted to the most general beginnings of mathematics. It goes back to Hausdorff’s classic Set Theory (2nd ed., 1927), where set theory and the theory of functions were expounded as the fundamental parts of mathematics in such a way that there was no need for references to other sources. Along the lines of Hausdorff’s initial work (1st ed., 1914), measure and integration theory is also included here as the third fundamental part of contemporary mathematics.The material about sets and numbers is placed in Volume 1 and the material about functions and measures is placed in Volume 2. Contents Fundamentals of the theory of classes, sets, and numbers Characterization of all natural models of Neumann – Bernays – Godel and Zermelo – Fraenkel set theories Local theory of sets as a foundation for category theory and its connection with the Zermelo – Fraenkel set theory Compactness theorem for generalized second-order language
Hausdorff Gaps And Limits
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Author : R. Frankiewicz
language : en
Publisher: Elsevier
Release Date : 1994-02-23
Hausdorff Gaps And Limits written by R. Frankiewicz and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-02-23 with Mathematics categories.
Gaps and limits are two phenomena occuring in the Boolean algebra P(&ohgr;)/fin. Both were discovered by F. Hausdorff in the mid 1930's. This book aims to show how they can be used in solving several kinds of mathematical problems and to convince the reader that they are of interest in themselves. The forcing technique, which is not commonly known, is used widely in the text. A short explanation of the forcing method is given in Chapter 11. Exercises, both easy and more difficult, are given throughout the book.