From the Preface to the first edition (1906): "A few of the most modern books on the Theory of Functions devote some pages to the establishment of certain results belonging to our subject, and required for the special purposes in hand... But we may fairly claim that the present work is the first attempt at a systematic exposition of the subject as a whole."

This undergraduate text develops its subject through observations of the physical world, covering finite sets, cardinal numbers, infinite cardinals, and ordinals. Includes exercises with answers. 1958 edition.

"This accessible approach to set theory for upper-level undergraduates poses rigorous but simple arguments. Each definition is accompanied by commentary that motivates and explains new concepts. A historical introduction is followed by discussions of classes and sets, functions, natural and cardinal numbers, the arithmetic of ordinal numbers, and related topics. 1971 edition with new material by the author"--

This monograph provides a unified and comprehensive treatment of an order-theoretic fixed point theory in partially ordered sets and its various useful interactions with topological structures. The material progresses systematically, by presenting the preliminaries before moving to more advanced topics. In the treatment of the applications a wide range of mathematical theories and methods from nonlinear analysis and integration theory are applied; an outline of which has been given an appendix chapter to make the book self-contained. Graduate students and researchers in nonlinear analysis, pure and applied mathematics, game theory and mathematical economics will find this book useful.

The theory of sets, described in the preface to this book as 'Georg Cantor's magnificent theory' was first developed in the 1870s, and was recognised as one of the most important new branches of mathematical science. W. H. Young and his wife Grace Chisholm Young wrote this book, published in 1906, as a 'simple presentation'; but they warn that it is effectively a work in progress: the writing 'has necessarily involved attempts to extend the frontier of existing knowledge, and to fill in gaps which broke the connexion between isolated parts of the subject.' The Young's were a dynamic force in mathematical research: William had been Grace's tutor at Girton College; she was subsequently the first woman to be awarded a Ph. D by the University of Göttingen. Cantor himself said of the book: 'It is a pleasure for me to see with what diligence, skill and success you have worked.'

This is an introductory undergraduate textbook in set theory. In mathematics these days, essentially everything is a set. Some knowledge of set theory is necessary part of the background everyone needs for further study of mathematics. It is also possible to study set theory for its own interest--it is a subject with intruiging results anout simple objects. This book starts with material that nobody can do without. There is no end to what can be learned of set theory, but here is a beginning.

Decomposable sets since T. R. Rockafellar in 1968 are one of basic notions in nonlinear analysis, especially in the theory of multifunctions. A subset K of measurable functions is called decomposable if (Q) for all and measurable A. This book attempts to show the present stage of "decomposable analysis" from the point of view of fixed point theory. The book is split into three parts, beginning with the background of functional analysis, proceeding to the theory of multifunctions and lastly, the decomposability property. Mathematicians and students working in functional, convex and nonlinear analysis, differential inclusions and optimal control should find this book of interest. A good background in fixed point theory is assumed as is a background in topology.