in this paper, we introduce the concepts of right, left and product stabilizers on hoops and study some properties and the relation between them.  and we try to find that how they can be equal and investigate that under what condition they can be filter, implicative filter, fantastic and positive implicative filter. also, we prove that  right and product stabilizers are filters and if they are ...

Let M be a smooth closed manifold. We will denote the group of all self-diffeomorphisms of M, with the smooth topology, by DIF F (M).

Solvothermal reactions of mixed ligands H(3)BTC and macrocyclic oxamide complexes (ML, M = Cu, Ni) with M(ClO(4))(2)·6H(2)O (M = Co, Zn, Ni and Cd) afford six new complexes, including [M'(4)(BTC)(2)(ML)(2)(OH)(2)(H(2)O)(2)]·2H(2)O (M' = Co, M = Ni, for (1); M' = Zn, M = Ni, for (2); M' = Zn, M = Cu, for (3)), [Ni(3)(BTC)(2)(NiL)(2)(H(2)O)(6)]·2CH(3)OH·2H(2)O (4), [Cd(4)(BTC)(2)(HBTC)(NiL)(4)(H(...

Various authors have considered the Zero-rest-mass equation and the contour integral representation of its solutions. Ferber generalized these equations to supertwistor spaces with 2N odd components so that with N=O we get the standard ungraded twistors of Penrose. In this paper we use the Batchelor theorem toconstruct the natural super Twistor space with coarse topology with underlying sta...

We review the history of modern immersion-theoretic topology during the period 1959–1973, beginning with the work of S. Smale followed by the important contributions from the Leningrad school of topology, including the work of M. Gromov. We discuss the development of the major geometrical ideas in immersion-theoretic topology during this period. Historical remarks are included and technical con...

The least cardinal λ such that some (equivalently: every) compact group with weight α admits a dense, pseudocompact subgroup of cardinality λ is denoted by m(α). Clearly, m(α) ≤ 2. We show: Theorem 3.3. Among groups of cardinality γ, the group ⊕γQ serves as a “test space” for the availability of a pseudocompact group topology in this sense: If m(α) ≤ γ ≤ 2 then ⊕γQ admits a (necessarily connect...

For Ω a Polish space we consider operator semigroups on the space Cb(Ω) of bounded, continuous functions and on the space M (Ω) of bounded Borel measures. The important fact here is that the dual of Cb(Ω) with the strict topology is M (Ω). We pursue the approach via bi-continuous semigroups, but we also show that the class of bi-continuous semigroups on Cb(Ω) with respect to the compact-open to...

In (2+1)-dimensional general relativity, the path integral for a manifold M can be expressed in terms of a topological invariant, the Ray-Singer torsion of a flat bundle over M . For some manifolds, this makes an explicit computation of transition amplitudes possible. In this paper, we evaluate the amplitude for a simple topology-changing process. We show that certain amplitudes for spatial top...

Take M , a finite-dimensional differentiable manifold, and f : M → R a smooth function. Such a function f is called a Morse function if it has no degenerate critical points. Morse theory allows us to connect the topology, in particular the homotopy type, of M with the behavior of f on M . In the following sections, we will state and prove two important theorems in Morse theory. Using these two ...

Let M be a von Neumann algebra, ' a faithful normal state and denote by M ' the xed point algebra of the modular group of '. Let U M and U M ' be the unitary groups of M and M '. In this paper we study the quotient U ' = U M =U M ' endowed with two natural topologies: the one induced by the usual norm of M (called here usual topology of U '), and the one induced by the pre-Hilbert C-module norm...