QUOTIENTS IN ALGEBRAIC AND SYMPLECTIC GEOMETRY 1
... objects may vary continuously. These types of spaces are known as moduli spaces and this is one of the motivations for constructing such quotients. For an action of a group G on a topological space X, we endow the set X/G := {G·x : x ∈ X} of G-orbits with the quotient topology; that is, the weakest ...
... objects may vary continuously. These types of spaces are known as moduli spaces and this is one of the motivations for constructing such quotients. For an action of a group G on a topological space X, we endow the set X/G := {G·x : x ∈ X} of G-orbits with the quotient topology; that is, the weakest ...
Algebraic K-theory of rings from a topological viewpoint
... The very beginning of algebraic K -theory is certainly due to some general considerations made by A. Grothendieck. He was motivated by his work in algebraic geometry and introduced the first K -theoretical notion in terms of category theory. His idea was to associate to a category C an abelian group ...
... The very beginning of algebraic K -theory is certainly due to some general considerations made by A. Grothendieck. He was motivated by his work in algebraic geometry and introduced the first K -theoretical notion in terms of category theory. His idea was to associate to a category C an abelian group ...
Topological vector spaces
... when |t| > 1/δ. If E satisfies the boundedness condition (1), then E ⊆ r W for some r ∈ R or C, as appropriate. This implies that E ⊆ t U when |t| > |r|/δ, as desired. Suppose that A and B are bounded subsets of V , and let us check that A∪B is also bounded. If U is an open set in V that contains 0, ...
... when |t| > 1/δ. If E satisfies the boundedness condition (1), then E ⊆ r W for some r ∈ R or C, as appropriate. This implies that E ⊆ t U when |t| > |r|/δ, as desired. Suppose that A and B are bounded subsets of V , and let us check that A∪B is also bounded. If U is an open set in V that contains 0, ...
An extension in fuzzy topological spaces
... that ÂA is the characteristic function of A, and the crisp topological space (X, [T ]) is called original topological space of (X; T ): De…nition 4 [13] A fuzzy topological space(X; T ) is called a week induction of the topological space (X; T0 ) if [T ] = T0 and each element of T is lower semi-cont ...
... that ÂA is the characteristic function of A, and the crisp topological space (X, [T ]) is called original topological space of (X; T ): De…nition 4 [13] A fuzzy topological space(X; T ) is called a week induction of the topological space (X; T0 ) if [T ] = T0 and each element of T is lower semi-cont ...
Elliptic spectra, the Witten genus, and the theorem of the cube
... In fact, it follows from formula (1.1) (for details see §2.7) that the q-expansion of this modular form is the Witten genus of M . The σ-orientation can therefore be viewed as a topological refinement of the Witten genus, and its modular invariance (1.3), an expression of the modular invariance of t ...
... In fact, it follows from formula (1.1) (for details see §2.7) that the q-expansion of this modular form is the Witten genus of M . The σ-orientation can therefore be viewed as a topological refinement of the Witten genus, and its modular invariance (1.3), an expression of the modular invariance of t ...
Covering space
In mathematics, more specifically algebraic topology, a covering map (also covering projection) is a continuous function p from a topological space, C, to a topological space, X, such that each point in X has an open neighbourhood evenly covered by p (as shown in the image); the precise definition is given below. In this case, C is called a covering space and X the base space of the covering projection. The definition implies that every covering map is a local homeomorphism.Covering spaces play an important role in homotopy theory, harmonic analysis, Riemannian geometry and differential topology. In Riemannian geometry for example, ramification is a generalization of the notion of covering maps. Covering spaces are also deeply intertwined with the study of homotopy groups and, in particular, the fundamental group. An important application comes from the result that, if X is a ""sufficiently good"" topological space, there is a bijection between the collection of all isomorphism classes of connected coverings of X and the conjugacy classes of subgroups of the fundamental group of X.