On linearly ordered H-closed topological semilattices

... τ is Hausdorff, so is τF . Also we base of a topology τF at the point x and since observe that the definition of τF implies that ↓e and ↑e are closed subsets of the topological space (F (E), τF ), and hence the semilattice operation on (F (E), τF ) is τ ) satisfies the conditions (i) and (iii) o ...

... τ is Hausdorff, so is τF . Also we base of a topology τF at the point x and since observe that the definition of τF implies that ↓e and ↑e are closed subsets of the topological space (F (E), τF ), and hence the semilattice operation on (F (E), τF ) is τ ) satisfies the conditions (i) and (iii) o ...

Maximal compact subgroups in the o-minimal setting

... The canonical projection π : G → G/N (G) induces an isomorphism between K and the maximal definable definably compact subgroup of G/N (G). Also P = A(G) × K is the smallest definable subgroup of G containing K, and [P, P ] = [K, K] is a maximal definable semisimple definably compact subgroup of G. C ...

... The canonical projection π : G → G/N (G) induces an isomorphism between K and the maximal definable definably compact subgroup of G/N (G). Also P = A(G) × K is the smallest definable subgroup of G containing K, and [P, P ] = [K, K] is a maximal definable semisimple definably compact subgroup of G. C ...

Conjugation spaces - Université de Genève

... additive maps, κ and σ are often easy to construct degree by degree. But we will show in the “multiplicativity theorem” in Section 3 that in fact σ and κ are ring homomorphisms. Moreover, given a C-equivariant map f : Y → X between spaces with involution, along with H ∗ -frames (σX , κX ) and (σY , ...

... additive maps, κ and σ are often easy to construct degree by degree. But we will show in the “multiplicativity theorem” in Section 3 that in fact σ and κ are ring homomorphisms. Moreover, given a C-equivariant map f : Y → X between spaces with involution, along with H ∗ -frames (σX , κX ) and (σY , ...

Positivity for toric vectorbundles

... σ is a maximal cone, then T acts on the fiber of Lw at xσ by χw . It is known that every equivariant line bundle on Uσ is equivariantly isomorphic to some Lw |Uσ , where the class of w in M/M ∩ σ ⊥ is uniquely determined. For every cone σ ∈ ∆, the restriction E|Uσ decomposes as a direct sum of equiv ...

... σ is a maximal cone, then T acts on the fiber of Lw at xσ by χw . It is known that every equivariant line bundle on Uσ is equivariantly isomorphic to some Lw |Uσ , where the class of w in M/M ∩ σ ⊥ is uniquely determined. For every cone σ ∈ ∆, the restriction E|Uσ decomposes as a direct sum of equiv ...

Common fixed point of mappings satisfying implicit contractive

... Huang and Zhang [14] reintroduced such spaces under the name of cone metric spaces and reintroduced definition of convergent and Cauchy sequences in the terms of interior points of the underlying cone. They also proved some fixed point results in framework of cone metric spaces. Subsequently, severa ...

... Huang and Zhang [14] reintroduced such spaces under the name of cone metric spaces and reintroduced definition of convergent and Cauchy sequences in the terms of interior points of the underlying cone. They also proved some fixed point results in framework of cone metric spaces. Subsequently, severa ...

EQUIVARIANT SYMMETRIC MONOIDAL STRUCTURES 1

... 5. Mackey Functors, Tambara Functors, and the transfer Much of this formalism arose from our attempt to understand the transfer. One approach in the finite group case is via the Wurtmuller map: G+ ∧H X −→ FH (G+ , X) for any H-spectrum X. This is a natural map arising from the the fact that G+ ∧H − ...

... 5. Mackey Functors, Tambara Functors, and the transfer Much of this formalism arose from our attempt to understand the transfer. One approach in the finite group case is via the Wurtmuller map: G+ ∧H X −→ FH (G+ , X) for any H-spectrum X. This is a natural map arising from the the fact that G+ ∧H − ...

PARTIAL DYNAMICAL SYSTEMS AND C∗

... is faithful if and only if it is faithful on C0 (X). This leads to a sufficient condition for simplicity of the reduced crossed product in Corollary 2.9. In Section 3 we consider invariant ideals of a partial action and the ideals they generate in the crossed product. In Proposition 3.1 we give a ge ...

... is faithful if and only if it is faithful on C0 (X). This leads to a sufficient condition for simplicity of the reduced crossed product in Corollary 2.9. In Section 3 we consider invariant ideals of a partial action and the ideals they generate in the crossed product. In Proposition 3.1 we give a ge ...

NSE CHARACTERIZATION OF THE SIMPLE GROUP L2(3n) Hosein

... 2. Notation and preliminaries For a natural number m, by π(m), we mean the set of all prime divisors of m, so it is obvious that if G is a finite group, then π(G) = π(|G|). A Sylow p-subgroup of G is denoted by Gp and by np (G), we mean the number of Sylow p-subgroups of G. Also, the largest element ...

... 2. Notation and preliminaries For a natural number m, by π(m), we mean the set of all prime divisors of m, so it is obvious that if G is a finite group, then π(G) = π(|G|). A Sylow p-subgroup of G is denoted by Gp and by np (G), we mean the number of Sylow p-subgroups of G. Also, the largest element ...

FROM COMMUTATIVE TO NONCOMMUTATIVE SETTINGS 1

... setting generalize. In [Sme13] this approach is, by means of divisorial one-sided ideal theory, extended to a class of semigroups that includes commutative and normalizing Krull monoids as special cases. In particular, this is applied to investigate factorizations in the semigroup of non zero-diviso ...

... setting generalize. In [Sme13] this approach is, by means of divisorial one-sided ideal theory, extended to a class of semigroups that includes commutative and normalizing Krull monoids as special cases. In particular, this is applied to investigate factorizations in the semigroup of non zero-diviso ...

A Course on Convex Geometry

... V . A is convex if it contains all the segments joining any two points of A, i.e. if x, y ∈ A and α ∈ [0, 1] implies that αx + (1 − α)y ∈ A. This simple algebraic property has surprisingly many and far-reaching consequences of geometric nature, but it also has topological consequences (if V carries ...

... V . A is convex if it contains all the segments joining any two points of A, i.e. if x, y ∈ A and α ∈ [0, 1] implies that αx + (1 − α)y ∈ A. This simple algebraic property has surprisingly many and far-reaching consequences of geometric nature, but it also has topological consequences (if V carries ...

An Introduction to Algebra and Geometry via Matrix Groups

... theory of vector spaces over arbitrary fields, and bilinear forms on such vector spaces. We can then define the orthogonal and symplectic group with respect to the bilinear forms. The tools we introduce allow us to determine the generators for the general linear group, the orthogonal group, the symp ...

... theory of vector spaces over arbitrary fields, and bilinear forms on such vector spaces. We can then define the orthogonal and symplectic group with respect to the bilinear forms. The tools we introduce allow us to determine the generators for the general linear group, the orthogonal group, the symp ...