Spaces with Non-Symmetric Distance
Author: Eugene M. Zaustinsky
Publisher: American Mathematical Soc.
Published: 1959
Total Pages: 98
ISBN-13: 0821812343
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Spaces with Non-symmetric Distance
Representation and Processing of Knowledge About Distances in Environmental Space
Author: Bettina Berendt
Publisher: IOS Press
Published: 1999
Total Pages: 284
ISBN-13: 9781586031107
DOWNLOAD EBOOK →Knowledge about distances---along with knowledge about spatial direction---is one of the most important fundamentals for a cognitive agent's orientation, navigation, and route planning. However, only some distances can be perceived directly. Therefore, knowledge about distances must often be inferred from other sources of information. In cognitive science research on spatial cognition, this is investigated in different ways, using empirical studies, computer simulations, and knowledge representation approaches. This book presents a comprehensive interdisciplinary study of human distance cognition. It discusses results on knowledge about distances from artificial intelligence research and cognitive psychology, proposing an integrating formal framework. Focusing on knowledge about route distances, it then presents a computational model of the way in which humans infer knowledge about distances in environmental spaces like cities or buildings.
The Geometry of Geodesics
Author: Herbert Busemann
Publisher: Courier Corporation
Published: 2012-07-12
Total Pages: 434
ISBN-13: 0486154629
DOWNLOAD EBOOK →A comprehensive approach to qualitative problems in intrinsic differential geometry, this text examines Desarguesian spaces, perpendiculars and parallels, covering spaces, the influence of the sign of the curvature on geodesics, more. 1955 edition. Includes 66 figures.
On Nonsymmetric Topological and Probabilistic Structures
Author: Yeol Je Cho
Publisher: Nova Publishers
Published: 2006
Total Pages: 230
ISBN-13: 9781594549175
DOWNLOAD EBOOK →In this book, generally speaking, some properties of bitopological spaces generated by certain non-symmetric functions are studied. These functions, called "probabilistic quasi-pseudo-metrics" and "fuzzy quasi-pseudo-metrics", are generalisations of classical quasi-pseudo metrics. For the sake of completeness as well as for convenience and easy comparison, most of the introductory paragraphs are mainly devoted to fundamental notions and results from the classical -- deterministic or symmetric -- theory.
Spaces with Non-systematic Distance
Author: Eugene Michael Zaustinsky
Publisher:
Published: 1959
Total Pages: 91
ISBN-13: 9780821899779
DOWNLOAD EBOOK →Recent Synthetic Differential Geometry
Author: Herbert Busemann
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 119
ISBN-13: 3642880576
DOWNLOAD EBOOK →A synthetic approach to intrinsic differential geometry in the large and its connections with the foundations of geometry was presented in "The Geometry of Geodesics" (1955, quoted as G). It is the purpose of the present report to bring this theory up to date. Many of the later ip.vestigations were stimulated by problems posed in G, others concern newtopics. Naturally references to G are frequent. However, large parts, in particular Chapters I and III as weIl as several individual seetions, use only the basic definitions. These are repeated here, sometimes in a slightly different form, so as to apply to more general situations. In many cases a quoted result is quite familiar in Riemannian Geometry and consulting G will not be found necessary. There are two exceptions : The theory of paralleIs is used in Sections 13, 15 and 17 without reformulating all definitions and properties (of co-rays and limit spheres). Secondly, many items from the literature in G (pp. 409-412) are used here and it seemed superfluous to include them in the present list of references (pp. 106-110). The quotations are distinguished by [ ] and ( ), so that, for example, FreudenthaI [1] and (I) are found, respectively, in G and here.
Topology
Author: K. Kuratowski
Publisher: Elsevier
Published: 2014-05-12
Total Pages: 581
ISBN-13: 1483272567
DOWNLOAD EBOOK →Topology, Volume I deals with topology and covers topics ranging from operations in logic and set theory to Cartesian products, mappings, and orderings. Cardinal and ordinal numbers are also discussed, along with topological, metric, and complete spaces. Great use is made of closure algebra. Comprised of three chapters, this volume begins with a discussion on general topological spaces as well as their specialized aspects, including regular, completely regular, and normal spaces. Fundamental notions such as base, subbase, cover, and continuous mapping, are considered, together with operations such as the exponential topology and quotient topology. The next chapter is devoted to the study of metric spaces, starting with more general spaces, having the limit as its primitive notion. The space is assumed to be metric separable, and this includes problems of cardinality and dimension. Dimension theory and the theory of Borei sets, Baire functions, and related topics are also discussed. The final chapter is about complete spaces and includes problems of general function theory which can be expressed in topological terms. The book includes two appendices, one on applications of topology to mathematical logics and another to functional analysis. This monograph will be helpful to students and practitioners of algebra and mathematics.
Handbook of the History of General Topology
Author: C.E. Aull
Publisher: Springer Science & Business Media
Published: 2013-04-18
Total Pages: 418
ISBN-13: 9401704708
DOWNLOAD EBOOK →This book is the first one of a work in several volumes, treating the history of the development of topology. The work contains papers which can be classified into 4 main areas. Thus there are contributions dealing with the life and work of individual topologists, with specific schools of topology, with research in topology in various countries, and with the development of topology in different periods. The work is not restricted to topology in the strictest sense but also deals with applications and generalisations in a broad sense. Thus it also treats, e.g., categorical topology, interactions with functional analysis, convergence spaces, and uniform spaces. Written by specialists in the field, it contains a wealth of information which is not available anywhere else.
Algebraical and Topological Foundations of Geometry
Author: Hans Freudenthal
Publisher: Elsevier
Published: 2014-05-09
Total Pages: 217
ISBN-13: 1483184641
DOWNLOAD EBOOK →Algebraical and Topological Foundations of Geometry contains the proceedings of the Colloquium on Algebraic and Topological Foundations of Geometry, held in Utrecht, the Netherlands in August 1959. The papers review the algebraical and topological foundations of geometry and cover topics ranging from the geometric algebra of the Möbius plane to the theory of parallels with applications to closed geodesies. Groups of homeomorphisms and topological descriptive planes are also discussed. Comprised of 26 chapters, this book introduces the reader to the theory of parallels with applications to closed geodesies; groups of homeomorphisms; complemented modular lattices; and topological descriptive planes. Subsequent chapters focus on collineation groups; exceptional algebras and exceptional groups; the connection between algebra and constructions with ruler and compasses; and the use of differential geometry and analytic group theory methods in foundations of geometry. Von Staudt projectivities of Moufang planes are also considered, and an axiomatic treatment of polar geometry is presented. This monograph will be of interest to students of mathematics.
