Quotient space

Ebook Topology: Part 1 presents the following content: Topological Spaces; Basis for Topology; The Order Topology; The Subspace Topology; Closed Sets and Limit Point; Continuous Functions;...Please refer to the documentation for more details.

158p chankora 16-06-2023 3 1   Download

Part 1 of lecture Topology presents the following content: general topology; infinite sets; topological space; continuity; connectedness; convergence; compactness; product of spaces; real functions and spaces of functions; quotient space;...

96p damtuyetha 09-01-2023 8 2   Download

Locally symmetric spaces play an important part in differential geometry and arise from many different areas such as topology, number theory, representation theory, algebraic geometry,...The typical important class consists of quotients of symmetric spaces by arithmetic groups, for example, the moduli space of elliptic curves is the quotient of the upper half plane H2 by SL(2, Z).

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We consider the categorical equivalence between crossed modules over groupoids and double groupoids with thin structures, and by this equivalence, we prove how normality and quotient concepts are related in these two categories and give some examples of these objects.

12p nutifooddau 21-01-2019 22 1   Download

In this paper, using generalized groups and their generalized actions, we define and study the notion of T-spaces. We study properties of the quotient space of a T-space and we present the conditions that imply the Hausdorff property for it. We also prove some essential results about topological generalized groups.

13p danhdanh27 07-01-2019 15 2   Download

We identify the symmetry algebra of the Laplacian on Euclidean space as an explicit quotient of the universal enveloping algebra of the Lie algebra of conformal motions. We construct analogues of these symmetries on a general conformal manifold. 1. Introduction The space of smooth first order linear differential operators on Rn that preserve harmonic functions is closed under Lie bracket. For n ≥ 3, it is finitedimensional (of dimension (n2 + 3n + 4)/2). Its commutator subalgebra is isomorphic to so(n + 1, 1), the Lie algebra of conformal motions of Rn .

22p noel_noel 17-01-2013 46 6   Download

The theory of automorphic functions in one complex variable was created during the second half of the nineteenth and the beginning of the twentieth centuries. Important contributions are due to such illustrious mathematicians as F. Klein, P. Koebe and H. Poincare. Two sources may be traced: the uniformization theory of algebraic functions, and certain topics in number theory. Automorphic functions with respect to groups with compact quotient space on the one hand and elliptic modular functions on the other are examples of these two aspects.

172p hotmoingay 03-01-2013 36 2   Download

One of the major advances of science in the 20th century was the discovery of a mathematical formulation of quantum mechanics by Heisenberg in 1925 [94].1 From a mathematical point of view, this transition from classical mechanics to quantum mechanics amounts to, among other things, passing from the commutative algebra of classical observables to the noncommutative algebra of quantum mechanical observables. To understand this better we recall that in classical mechanics an observable of a system (e.g. energy, position, momentum, etc.

239p thienbinh1311 13-12-2012 48 4   Download

Distribution in the Body proceeds rapidly, because the absorbing surface is greatly enlarged due to the formation of the epithelial brush border (submicroscopic foldings of the plasmalemma). The absorbability of a drug is characterized by the absorption quotient, that is, the amount absorbed divided by the amount in the gut available for absorption. In the respiratory tract, cilia-bearing epithelial cells are also joined on the luminal side by zonulae occludentes, so that the bronchial space and the interstitium are separated by a continuous phospholipid barrier.

10p bigbaby87 04-09-2010 130 20   Download