In algebraic topology, a branch of mathematics, a spectrum is an object representing a generalized cohomology theory. Every such cohomology theory is...

commutative ring (called the spectrum of the ring) a topological space. The Zariski topology allows tools from topology to be used to study algebraic...

considers what he calls the patch topology on a prime spectrum. By definition, the patch topology is the smallest topology in which the sets of the forms...

characterizations of the topology on the spectrum in terms of positive definite functions are desirable. In fact, the topology on  is intimately connected...

mathematical logic Spectrum of a theory, in mathematical logic There are also several other, unrelated meanings: Spectrum (topology), the fundamental object...

Network (MCN) The plural of spectrum (topology), an object representing a generalized cohomology theory in algebraic topology Spectra (mathematical association)...

Network topology is the arrangement of the elements (links, nodes, etc.) of a communication network. Network topology can be used to define or describe...

a topology native to it, and this can be extended to vector spaces over that field. The Zariski topology is defined algebraically on the spectrum of...

given the relative weak-* topology. This is the topology of pointwise convergence. A net {fk}k of elements of the spectrum of A converges to f if and...

topology τ of a topological space (X, τ) is a family B {\displaystyle {\mathcal {B}}} of open subsets of X such that every open set of the topology is...

properties and concepts in algebraic topology in mathematics. See also: glossary of topology, list of algebraic topology topics, glossary of category theory...

Stable homotopy theory Spectrum (homotopy theory) Morava K-theory Hodge conjecture Weil conjectures Directed algebraic topology Example: DE-9IM Chain complex...

general topology (or point set topology) is the branch of topology that deals with the basic set-theoretic definitions and constructions used in topology. It...

In mathematics, specifically general topology, compactness is a property that seeks to generalize the notion of a closed and bounded subset of Euclidean...

concept of the spectrum of a bounded operator is a generalization of the eigenvalue concept for matrices. In algebraic topology, a spectrum is an object...

In topology and related branches of mathematics, a T1 space is a topological space in which, for every pair of distinct points, each has a neighborhood...

and algebraic geometry, in particular as the Zariski topology on an algebraic variety or the spectrum of a ring. They also arise in the model theory of intuitionistic...

Brazilian mathematician whose research concerned differential topology, algebraic topology, and differential geometry. Lima was an influential figure in...

Connected and disconnected subspaces of R² In topology and related branches of mathematics, a connected space is a topological space that cannot be represented...

{\displaystyle {\mathcal {A}}_{p}} -structure. Adams spectral sequence Spectrum (topology) Homotopy groups of spheres Adams, J. Frank (John Frank) (1974). Stable...

construction (named after René Thom and Lev Pontryagin) of algebraic topology and differential topology is a topological space associated to a vector bundle, over...

The radio spectrum is the part of the electromagnetic spectrum with frequencies from 3 Hz to 3,000 GHz (3 THz). Electromagnetic waves in this frequency...

ideals of A. Then there is a topology on Prim ⁡ ( A ) {\displaystyle \operatorname {Prim} (A)} , called the Jacobson topology, defined so that the closure...

In the mathematical discipline of topology, the Brown–Gitler spectrum is a spectrum whose cohomology is a certain cyclic module over the Steenrod algebra...

primarily by its curvature, while the global geometry is characterised by its topology (which itself is constrained by curvature). General relativity explains...

Gray's conjecture List of topologies Loop group Path (topology) Quasigroup Spectrum (topology) Path space (algebraic topology) May, J. P. (1999), A Concise...

metrizable; important examples include the Zariski topology on an algebraic variety or on the spectrum of a ring, used in algebraic geometry, the topological...

bandforms that can differ in different parts of the frequency spectrum. The mm'-type topology can be thought of as a double m-type design. Like the m-type...

with the discrete topology. Proof: Every subset of X is compact in a Hausdorff space, hence closed. So X has the discrete topology, and being compact...

the multiplication operation is continuous with respect to the metric topology. A Banach algebra is called unital if it has an identity element for the...