Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

The purpose of this unique book is to establish purely algebraic foundations for the development of certain parts of topology. Some topologists seek to understand geometric properties of solutions to finite systems of equations or inequalities and configurations which in some sense actually occur in the real world. Others study spaces constructed more abstractly using infinite limit processes. Their goal is to determine just how similar or different these abstract spaces are from those which are finitely described. However, as topology is usually taught, even the first, more concrete type of problem is approached using the language and methods of the second type. Professor Brumfiel's thesis is that this is unnecessary and, in fact, misleading philosophically. He develops a type of algebra, partially ordered rings, in which it makes sense to talk about solutions of equations and inequalities and to compare geometrically the resulting spaces. The importance of this approach is primarily that it clarifies the sort of geometrical questions one wants to ask and answer about those spaces which might have physical significance.

Categories (Mathematics) --- Commutative rings. --- Rings (Algebra) --- Category theory (Mathematics) --- Algebra, Homological --- Algebra, Universal --- Group theory --- Logic, Symbolic and mathematical --- Topology --- Functor theory --- Commutative rings --- 512.7 --- 512.7 Algebraic geometry. Commutative rings and algebras --- Algebraic geometry. Commutative rings and algebras --- Categories (Mathematics). --- Ordered algebraic structures --- Algebraic geometry --- Anneaux commutatifs --- Catégories (Mathématiques) --- Anneaux (algèbre) --- Géométrie algébrique --- Structures algébriques ordonnées

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Over the past several decades, the territory of preserver problems has been continuously enlarging within the frame of linear analysis. The aim of this work is to present a sort of cross-section of the modern theory of preservers on infinite dimensional spaces (operator spaces and function spaces) through the author's corresponding results. Special emphasis is put on preserver problems concerning some structures of Hilbert space operators which appear in quantum mechanics. Moreover, local automorphisms and local isometries of operator algebras and function algebras are discussed in details.

Operatortheorie. --- Functieruimten. --- Kwantummechanica. --- Ordered algebraic structures. --- Operator algebras. --- Function spaces. --- Linear operators. --- Structures algébriques ordonnées --- Algèbres d'opérateurs --- Espaces fonctionnels --- Opérateurs linéaires --- Algebras, Linear. --- Electronic books. -- local. --- Linear operators -- Mathematics. --- Quantum theory -- Mathematics. --- Ordered algebraic structures --- Operator algebras --- Function spaces --- Linear operators --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Theory --- Algebra --- Calculus --- Linear maps --- Maps, Linear --- Operators, Linear --- Spaces, Function --- Algebras, Operator --- Algebraic structures, Ordered --- Structures, Ordered algebraic --- Mathematics. --- Functional analysis. --- Mathematical logic. --- Quantum physics. --- Mathematical Logic and Foundations. --- Mathematics, general. --- Functional Analysis. --- Quantum Physics. --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Physics --- Mechanics --- Thermodynamics --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Math --- Science --- Quantum theory --- Linear algebra --- Algebra, Universal --- Generalized spaces --- Mathematical analysis --- Calculus of operations --- Line geometry --- Topology --- Operator theory --- Logic, Symbolic and mathematical. --- Quantum theory. --- Functional analysis --- Topological algebras