Results 151 to 160 of about 126,856 (194)

Categorical Structure of Closure Operators with Applications to Topology, Algebra and Mathematics and its Applications,

1995
Offers an extensive investigation of the theory of closure operators in different areas of mathematics, including (but not limited to) algebra, topology, combinatorics, etc. The closure operators are used to describe relevant concepts and properties as epimorphisms, injectivity, compactness, (dis)connectedness, torsion theories, factoriaztion systems ...
DIKRANJAN, Dikran, THOLEN W.
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Exploring the Applications of Algebraic Topology in Modern Mathematics and Data Analysis

Algebraic topology is a vibrant and intricate branch of mathematics that intertwines the abstract structures of algebra with the intuitive notions of topology. At its core, algebraic topology investigates topological spaces and their properties through algebraic invariants, enabling mathematicians to classify and understand spaces in a profound way ...
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Algebra, Geometry, Topology, and Functional Analysis Equations of Major Unsolved Problems in Mathematics

(Hodge Conjecture). Description: Let X be a smooth projective complexalgebraic variety. Its cohomology admits a Hodge decomposition:H2k(X, C) = Mp+q=2kHp,q(X).Conjecture: Every class inHk,k(X) ∩ H2k(X, Q)is a rational linear combination of classes of algebraic cycles.2Problem 1.2 (Jacobian Conjecture). Description: Let F = (F1, . . . , Fn) : Cn → Cn be
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Exceptional topology of non-Hermitian systems

Reviews of Modern Physics, 2021
Emil J Bergholtz, Jan Carl Budich, Flore K Kunst   +2 more
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Higher-order band topology

Nature Reviews Physics, 2021
Bi-Ye Xie, Hai-Xiao Wang, Xiujuan Zhang
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BUILDING MATHEMATICAL MATURITY THROUGH ALGEBRAIC TOPOLOGY CHALLENGING PATHS

A central educational goal of higher-level mathematics undergraduate courses is to foster the development of competences that enable students to use mathematical abstraction and formalism and, at the same time, to develop mathematical creativity. Does it mean mathematical maturity? Research in university mathematics education suggests that to grasp the
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Non-Hermitian topology and exceptional-point geometries

Nature Reviews Physics, 2022
Kun Ding, Chen Fang, Guancong
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International Series of Monographs in Pure and Applied Mathematics. Vol. 1. An Introduction to Algebraic Topology.

The American Mathematical Monthly, 1958
Dick Wick Hall, A. H. Wallace
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A Note on the Relationship Between Boolean Algebra, Mathematical Logic, Set Theory, Topology, and Probability Theory

, 2021
Elmar Guseinov
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Topology and geometry under the nonlinear electromagnetic spotlight

Nature Materials, 2021
Qiong, Adolfo G G Grushin, Kenneth S Burch   +2 more
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