Author: Sagvan Y. Musa Publisher: Infinite Study ISBN: Category : Mathematics Languages : en Pages : 16
Book Description
According to its definition, a topological space could be a highly unexpected object. There are spaces (indiscrete space) which have only two open sets: the empty set and the entire space. In a discrete space, on the other hand, each set is open. These two artificial extremes are very rarely seen in actual practice. Most spaces in geometry and analysis fall somewhere between these two types of spaces. Accordingly, the separation axioms allow us to say with confidence whether a topological space contains a sufficient number of open sets to meet our needs. To this end, we use bipolar hypersoft (BHS) sets (one of the efficient tools to deal with ambiguity and vagueness) to define a new kind of separation axioms called BHS e Ti-space (i = 0, 1, 2, 3, 4).
Author: Carlos R. Borges Publisher: World Scientific ISBN: 9789810242404 Category : Mathematics Languages : en Pages : 224
Book Description
Based on the theme that topology is really the universal language of modern mathematics, Borges (mathematics, U. of California-Davis) introduces it to students who have a good grasp of fundamentals of logic, set theory, elementary analysis, and group theory. He gets rapidly to applications. His goal is to prepare students for further study in mathematics. He does not include bibliographic references. Annotation copyrighted by Book News, Inc., Portland, OR
Author: Ying-ming Liu Publisher: World Scientific ISBN: 9814518204 Category : Mathematics Languages : en Pages : 365
Book Description
Fuzzy set theory provides us with a framework which is wider than that of classical set theory. Various mathematical structures, whose features emphasize the effects of ordered structure, can be developed on the theory. Fuzzy topology is one such branch, combining ordered structure with topological structure. This branch of mathematics, emerged from the background — processing fuzziness, and locale theory, proposed from the angle of pure mathematics by the great French mathematician Ehresmann, comprise the two most active aspects of topology on lattice, which affect each other.This book is the first monograph to systematically reflect the up-to-date state of fuzzy topology. It emphasizes the so-called “pointed approach” and the effects of stratification structure appearing in fuzzy sets.The monograph can serve as a reference book for mathematicians, researchers, and graduate students working in this branch of mathematics. After an appropriate rearrangements of the chapters and sections, it can also be used as a text for undergraduates.
Author: O. Ya. Viro, O. A. Ivanov, N. Yu. Netsvetaev, V. M. Kharlamov Publisher: American Mathematical Soc. ISBN: 9780821886250 Category : Mathematics Languages : en Pages : 432
Book Description
This text contains a detailed introduction to general topology and an introduction to algebraic topology via its most classical and elementary segment. Proofs of theorems are separated from their formulations and are gathered at the end of each chapter, making this book appear like a problem book and also giving it appeal to the expert as a handbook. The book includes about 1,000 exercises.
Author: C.E. Aull Publisher: Springer Science & Business Media ISBN: 9401704708 Category : Mathematics Languages : en Pages : 418
Book Description
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.
Author: Çigdem GÜNÜUZ ARAS Publisher: Infinite Study ISBN: Category : Mathematics Languages : en Pages : 13
Book Description
A neutrosophic set, proposed by Smarandache, considers a truth membership function, an indeterminacy membership function, and a falsity membership function. Neutrosophic soft sets combined by Maji have been utilized successfully to model uncertainty in several areas of application such as control, reasoning, pattern recognition, and computer vision. In the present paper, some basic notions of neutrosophic soft sets have been redefined and the neutrosophic soft point concept has been introduced. Later we give the neutrosophic soft Ti -space and the relationships between them are discussed in detail.
Author: Lynn Arthur Steen Publisher: Courier Corporation ISBN: 0486319296 Category : Mathematics Languages : en Pages : 274
Book Description
Over 140 examples, preceded by a succinct exposition of general topology and basic terminology. Each example treated as a whole. Numerous problems and exercises correlated with examples. 1978 edition. Bibliography.
Author: Michael C. Gemignani Publisher: Courier Corporation ISBN: 9780486665221 Category : Mathematics Languages : en Pages : 292
Book Description
Topology is one of the most rapidly expanding areas of mathematical thought: while its roots are in geometry and analysis, topology now serves as a powerful tool in almost every sphere of mathematical study. This book is intended as a first text in topology, accessible to readers with at least three semesters of a calculus and analytic geometry sequence. In addition to superb coverage of the fundamentals of metric spaces, topologies, convergence, compactness, connectedness, homotopy theory, and other essentials, Elementary Topology gives added perspective as the author demonstrates how abstract topological notions developed from classical mathematics. For this second edition, numerous exercises have been added as well as a section dealing with paracompactness and complete regularity. The Appendix on infinite products has been extended to include the general Tychonoff theorem; a proof of the Tychonoff theorem which does not depend on the theory of convergence has also been added in Chapter 7.
Author: Felix Hausdorff Publisher: American Mathematical Soc. ISBN: 1470464942 Category : Education Languages : en Pages : 352
Book Description
This work is a translation into English of the Third Edition of the classic German language work Mengenlehre by Felix Hausdorff published in 1937. From the Preface (1937): “The present book has as its purpose an exposition of the most important theorems of the theory of sets, along with complete proofs, so that the reader should not find it necessary to go outside this book for supplementary details while, on the other hand, the book should enable him to undertake a more detailed study of the voluminous literature on the subject. The book does not presuppose any mathematical knowledge beyond the differential and integral 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 … The mathematician will … find in this book some things that will be new to him, at least as regards formal presentation and, in particular, as regards the strengthening of theorems, the simplification of proofs, and the removal of unnecessary hypotheses.”
Author: Sagvan Y. Musa
Author: Carlos R. Borges
Author: Ying-ming Liu
Author: O. Ya. Viro, O. A. Ivanov, N. Yu. Netsvetaev, V. M. Kharlamov
Author: C.E. Aull
Author: Çigdem GÜNÜUZ ARAS 
Author: Lynn Arthur Steen
Author: Seymour Lipschutz
Author: Michael C. Gemignani
Author: Felix Hausdorff