Topology

Topology has been referred to as "e;rubber-sheet geometry"e; .

This is a foundation for arithmetic topology - a new branch of mathematics which is focused upon the analogy between knot theory and number theory.

Discrete dynamical systems are essentially iterated functions.

We have inserted, in this edition, an extra chapter (Chapter X) entitled "e;Some Applications and Recent Developments.

This book is an introduction to manifolds at the beginning graduate level.

This book offers a presentation of the special theory of relativity that is mathematically rigorous and yet spells out in considerable detail the physical significance of the mathematics.

Banach spaces provide a framework for linear and nonlinear functional analysis, operator theory, abstract analysis, probability, optimization and other branches of mathematics.

The theory of function spaces endowed with the topology of point wise convergence, or Cp-theory, exists at the intersection of three important areas of mathematics: topological algebra, functional analysis, and general topology.

Manifolds, the higher-dimensional analogs of smooth curves and surfaces, are fundamental objects in modern mathematics.

This is a book in pure mathematics dealing with homotopy theory, one of the main branches of algebraic topology.

This is a book on topology and geometry and, like any books on subjects as vast as these, it has a point-of-view that guided the selection of topics.

Simplicial Structures in Topology provides a clear and comprehensive introduction to the subject.

The first of three volumes on partial differential equations, this one introduces basic examples arising in continuum mechanics, electromagnetism, complex analysis and other areas, and develops a number of tools for their solution, in particular Fourier analysis, distribution theory, and Sobolev spaces.

This IMA Volume in Mathematics and its Applications TOWARDS HIGHER CATEGORIES contains expository and research papers based on a highly successful IMA Summer Program on n-Categories: Foundations and Applications.

Althoughsubmanifoldscomplexmanifoldshasbeenanactive?

The body of work presented in this book comes from research carried out since 2017 as part of the international "e;Actualite de Rene Thom"e; project.

From a Geometrical Point of View explores historical and philosophical aspects of category theory, trying therewith to expose its significance in the mathematical landscape.

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A spatial logic is a formal language interpreted over any class of structures featuring geometrical entities and relations, broadly construed.

This book is an attempt to give a systematic presentation of results and me- ods which concern the ?

The notion of a ?

The papers collected in this volume are contributions to the 43rd session of the Seminaire ' de mathematiques ' superieures ' (SMS) on "e;Morse Theoretic Methods in Nonlinear Analysis and Symplectic Topology.

The emergence of topological quantum ?

This book is based on the lecture notes from a course we taught at Penn State University during the fall of 2002.

Over the field of real numbers, analytic geometry has long been in deep interaction with algebraic geometry, bringing the latter subject many of its topological insights.

One of the most important mathematical achievements of the past several decades has been A.

In this book, Claire Voisin provides an introduction to algebraic cycles on complex algebraic varieties, to the major conjectures relating them to cohomology, and even more precisely to Hodge structures on cohomology.

The Shape of Space, Third Edition maintains the standard of excellence set by the previous editions.

The Shape of Space, Third Edition maintains the standard of excellence set by the previous editions.

Many of the modern variational problems in topology arise in different but overlapping fields of scientific study: mechanics, physics and mathematics.

Many of the modern variational problems in topology arise in different but overlapping fields of scientific study: mechanics, physics and mathematics.

This is the first textbook on C*-algebra theory with a view toward Noncommutative Geometry.

Originally published in 1984.

Originally published in 1984.

An up to date study of recent progress in vector bundle methods in the representation theory of elementary abelian groups.

An up to date study of recent progress in vector bundle methods in the representation theory of elementary abelian groups.

Classroom-tested and featuring over 100 exercises, this text introduces the key algebraic geometry field of Hurwitz theory.

Classroom-tested and featuring over 100 exercises, this text introduces the key algebraic geometry field of Hurwitz theory.

Simple enough for detailed study, rich enough to show interesting behavior, K3 surfaces illuminate core methods in algebraic geometry.

Simple enough for detailed study, rich enough to show interesting behavior, K3 surfaces illuminate core methods in algebraic geometry.

This second volume shows how factorization algebras arise from interacting field theories, both classical and quantum.

This first volume develops factorization algebras with a focus upon examples exhibiting their use in field theory, which will be useful for researchers and graduates.

This first volume develops factorization algebras with a focus upon examples exhibiting their use in field theory, which will be useful for researchers and graduates.

This book brings together several directions of work in model theory between the late 1950s and early 1980s.