Selection Principles And Covering Properties In Topology
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Selection Principles And Covering Properties In Topology
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Author : Ljubiša D. R. Kočinac
language : en
Publisher:
Release Date : 2006
Selection Principles And Covering Properties In Topology written by Ljubiša D. R. Kočinac and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Music categories.
Recent Progress In General Topology Iii
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Author : K.P. Hart
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-11
Recent Progress In General Topology Iii written by K.P. Hart 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 2013-12-11 with Mathematics categories.
The book presents surveys describing recent developments in most of the primary subfields of General Topology, and its applications to Algebra and Analysis during the last decade, following the previous editions (North Holland, 1992 and 2002). The book was prepared in connection with the Prague Topological Symposium, held in 2011. During the last 10 years the focus in General Topology changed and therefore the selection of topics differs from that chosen in 2002. The following areas experienced significant developments: Fractals, Coarse Geometry/Topology, Dimension Theory, Set Theoretic Topology and Dynamical Systems.
Open Problems In Topology Ii
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Author : Elliott M. Pearl
language : en
Publisher: Elsevier
Release Date : 2011-08-11
Open Problems In Topology Ii written by Elliott M. Pearl and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-11 with Mathematics categories.
This volume is a collection of surveys of research problems in topology and its applications. The topics covered include general topology, set-theoretic topology, continuum theory, topological algebra, dynamical systems, computational topology and functional analysis.* New surveys of research problems in topology* New perspectives on classic problems* Representative surveys of research groups from all around the world
Advanced Topics Of Topology
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Author : Francisco Bulnes
language : en
Publisher: BoD – Books on Demand
Release Date : 2022-07-27
Advanced Topics Of Topology written by Francisco Bulnes and has been published by BoD – Books on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-07-27 with Mathematics categories.
Topology is an area of mathematics that establishes relations and transformations between spaces with a certain structure depending on their position and considering the structure of the ambient space where these relations exist. This book discusses various concepts and theories of topology, including diffeomorphisms, immersions, Hausdorff spaces, cobordisms, homotopy theory, symplectic manifolds, topology of quantum field theory, algebraic varieties, dimension theory, Koszul complexes, continuum theory, and metrizability, among others.
Summability Fixed Point Theory And Generalized Integrals With Applications
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Author : Hemanta Kalita
language : en
Publisher: CRC Press
Release Date : 2025-06-19
Summability Fixed Point Theory And Generalized Integrals With Applications written by Hemanta Kalita and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-06-19 with Mathematics categories.
This book presents contemporary mathematical concepts and techniques including theories of summability, fixed point and non-absolute integration and applications, providing an overview of recent developments in the foundations of the field as well as its applications. It discusses the recent results of double sequence spaces as the four-dimensional forward difference matrix in double sequence spaces, several new fixed point on Hadamard type fractional integral and differential operator related to the qualitative properties of solutions like, existence and uniqueness, stability, continuous dependence, controllability, oscillations, etc. It also includes several new areas of nonabsolute integration theory are introduced and their applications to other fields. This reference text is for researchers, academics, and professionals in the field of pure and applied mathematics. • Covers recent research breakthroughs in this field offering new approaches and methods for both theoretical exploration and practical application • Presents insights into functional analytic methods in summability, absolute and strong summability, direct theorems on summability, special and general summability methods, and their applications • Highlights fixed-point theory’s application to real-world problems and offers solutions to various complex challenges • Introduces new areas of non-absolute integration theory, such as the Henstock-Kurzweil integral and generalized Riemann integral • Discusses sequence spaces and functional analysis, including the exploration of double sequence spaces and the four-dimensional forward difference matrix, offering valuable contributions to ongoing research.
Set Theory And Its Applications
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Author : Liljana Babinkostova
language : en
Publisher: American Mathematical Soc.
Release Date : 2011
Set Theory And Its Applications written by Liljana Babinkostova 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 2011 with Mathematics categories.
This book consists of several survey and research papers covering a wide range of topics in active areas of set theory and set theoretic topology. Some of the articles present, for the first time in print, knowledge that has been around for several years and known intimately to only a few experts. The surveys bring the reader up to date on the latest information in several areas that have been surveyed a decade or more ago. Topics covered in the volume include combinatorial and descriptive set theory, determinacy, iterated forcing, Ramsey theory, selection principles, set-theoretic topology, and universality, among others. Graduate students and researchers in logic, especially set theory, descriptive set theory, and set-theoretic topology, will find this book to be a very valuable reference.
The Structure Of The Real Line
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Author : Lev Bukovský
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-03-02
The Structure Of The Real Line written by Lev Bukovský 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 2011-03-02 with Mathematics categories.
The rapid development of set theory in the last fifty years, mainly by obtaining plenty of independence results, strongly influenced an understanding of the structure of the real line. This book is devoted to the study of the real line and its subsets taking into account the recent results of set theory. Whenever possible the presentation is done without the full axiom of choice. Since the book is intended to be self-contained, all necessary results of set theory, topology, measure theory, and descriptive set theory are revisited with the purpose of eliminating superfluous use of an axiom of choice. The duality of measure and category is studied in a detailed manner. Several statements pertaining to properties of the real line are shown to be undecidable in set theory. The metamathematics behind set theory is shortly explained in the appendix. Each section contains a series of exercises with additional results.
A Cp Theory Problem Book
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Author : Vladimir V. Tkachuk
language : en
Publisher: Springer
Release Date : 2016-04-05
A Cp Theory Problem Book written by Vladimir V. Tkachuk and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-05 with Mathematics categories.
This fourth volume in Vladimir Tkachuk's series on Cp-theory gives reasonably complete coverage of the theory of functional equivalencies through 500 carefully selected problems and exercises. By systematically introducing each of the major topics of Cp-theory, the book is intended to bring a dedicated reader from basic topological principles to the frontiers of modern research. The book presents complete and up-to-date information on the preservation of topological properties by homeomorphisms of function spaces. An exhaustive theory of t-equivalent, u-equivalent and l-equivalent spaces is developed from scratch. The reader will also find introductions to the theory of uniform spaces, the theory of locally convex spaces, as well as the theory of inverse systems and dimension theory. Moreover, the inclusion of Kolmogorov's solution of Hilbert's Problem 13 is included as it is needed for the presentation of the theory of l-equivalent spaces. This volume contains the most important classical results on functional equivalencies, in particular, Gul'ko and Khmyleva's example of non-preservation of compactness by t-equivalence, Okunev's method of constructing l-equivalent spaces and the theorem of Marciszewski and Pelant on u-invariance of absolute Borel sets.
Mathematical Analysis And Applications
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Author : Michael Ruzhansky
language : en
Publisher: John Wiley & Sons
Release Date : 2018-04-05
Mathematical Analysis And Applications written by Michael Ruzhansky and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-04-05 with Mathematics categories.
An authoritative text that presents the current problems, theories, and applications of mathematical analysis research Mathematical Analysis and Applications: Selected Topics offers the theories, methods, and applications of a variety of targeted topics including: operator theory, approximation theory, fixed point theory, stability theory, minimization problems, many-body wave scattering problems, Basel problem, Corona problem, inequalities, generalized normed spaces, variations of functions and sequences, analytic generalizations of the Catalan, Fuss, and Fuss–Catalan Numbers, asymptotically developable functions, convex functions, Gaussian processes, image analysis, and spectral analysis and spectral synthesis. The authors—a noted team of international researchers in the field— highlight the basic developments for each topic presented and explore the most recent advances made in their area of study. The text is presented in such a way that enables the reader to follow subsequent studies in a burgeoning field of research. This important text: Presents a wide-range of important topics having current research importance and interdisciplinary applications such as game theory, image processing, creation of materials with a desired refraction coefficient, etc. Contains chapters written by a group of esteemed researchers in mathematical analysis Includes problems and research questions in order to enhance understanding of the information provided Offers references that help readers advance to further study Written for researchers, graduate students, educators, and practitioners with an interest in mathematical analysis, Mathematical Analysis and Applications: Selected Topics includes the most recent research from a range of mathematical fields.
Centenary Of The Borel Conjecture
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Author : Marion Scheepers
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-09-04
Centenary Of The Borel Conjecture written by Marion Scheepers 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 2020-09-04 with Education categories.
Borel's Conjecture entered the mathematics arena in 1919 as an innocuous remark about sets of real numbers in the context of a new covering property introduced by Émile Borel. In the 100 years since, this conjecture has led to a remarkably rich adventure of discovery in mathematics, producing independent results and the discovery of countable support iterated forcing, developments in infinitary game theory, deep connections with infinitary Ramsey Theory, and significant impact on the study of topological groups and topological covering properties. The papers in this volume present a broad introduction to the frontiers of research that has been spurred on by Borel's 1919 conjecture and identify fundamental unanswered research problems in the field. Philosophers of science and historians of mathematics can glean from this collection some of the typical trends in the discovery, innovation, and development of mathematical theories.