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In mathematics, particularly topology, an atlas is a concept used to describe a manifold. An atlas consists of individual charts that, roughly speaking...

real affine spaces. The Zariski topology of an algebraic variety is the topology whose closed sets are the algebraic subsets of the variety. In the case...

specifically in differential topology, Morse theory enables one to analyze the topology of a manifold by studying differentiable functions on that manifold....

for the 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...

finite-dimensional Euclidean spaces. They were introduced by Alexander Grothendieck. The topology on nuclear spaces can be defined by a family of seminorms whose unit...

of subsets which are considered "closed". These two ways of defining the topology are essentially equivalent because the complement of an open set is closed...

like a torus. To date, no compelling evidence has been found suggesting the topology of the universe is not simply connected, though it has not been ruled...

× X → [ 0 , ∞ ) {\displaystyle d:X\times X\to [0,\infty )} such that the topology induced by d {\displaystyle d} is τ . {\displaystyle \tau .} Metrization...

case) having determinant 1. Thus the topology of the group SL(n, C) is the product of the topology of SU(n) and the topology of the group of hermitian matrices...

G {\displaystyle {\mathcal {G}}} (e.g. the "topology of uniform convergence on compact sets" or the "topology of compact convergence", see the footnote...

sets. These conditions guarantee that the measure is "compatible" with the topology of the space, and most measures used in mathematical analysis and in...

Mackey space is a locally convex topological vector space X such that the topology of X coincides with the Mackey topology τ(X,X′), the finest topology...

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

context, and it may refer to: the final topology on the disjoint union the topology arising from a norm the strong operator topology the strong topology...

(discussed below). The topology of every Fréchet space is induced by some translation-invariant complete metric. Conversely, if the topology of a locally convex...

following: the detailed study of subsets of the real line (once known as the topology of point sets; this usage is now obsolete) the introduction of the manifold...

important area is molecular knot theory and circuit topology that describe the topology of folded linear molecules such as proteins and nucleic acids. The history...

elements of the 0-dimensional complex (the points). The topology of the CW complex is the topology of the quotient space defined by these gluing maps....

topology on X (resp. on Y) with respect to the canonical pairing ⟨X, Y⟩. The topology σ(X,Y) is the initial topology of X with respect to Y. If Y is a vector...

and hosts, and the transmission lines between them, form a graph with the topology of a star. Data on a star network passes through the hub before continuing...