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1.
Let be a disjoint iteration group on the unit circle , that is a family of homeomorphisms such that F v1F v2 = F v1+v2 for v 1, v 2V and each F v either is the identity mapping or has no fixed point ((V, +) is a 2-divisible nontrivial Abelian group). Denote by the set of all cluster points of {F v (z), vV} for . In this paper we give a general construction of disjoint iteration groups for which .  相似文献   

2.
For an ℓ-cyclically ordered set M with the ℓ-cyclic order C let P(M) be the set of all monotone permutations on M. We define a ternary relation on the set P(M). Further, we define in a natural way a group operation (denoted by ·) on P(M). We prove that if the ℓ-cyclic order C is complete and ≠ 0, then (P(M),·, ) is a half cyclically ordered group.  相似文献   

3.
Let S be a regular semigroup and E(S) be the set of its idempotents. We call the sets S(e, f)f and eS(e, f) one-sided sandwich sets and characterize them abstractly where e, fE(S). For a, a′ ∈ S such that a = aa′a, a′ = a′aa′, we call S(a) = S(a′a, aa′) the sandwich set of a. We characterize regular semigroups S in which all S(e; f) (or all S(a)) are right zero semigroups (respectively are trivial) in several ways including weak versions of compatibility of the natural order. For every aS, we also define E(a) as the set of all idempotets e such that, for any congruence ϱ on S, aϱa 2 implies that aϱe. We study the restrictions on S in order that S(a) or be trivial. For , we define on S by a b if . We establish for which S are or congruences.  相似文献   

4.
In this paper we prove two results. The first is an extension of the result of G. D. Jones [4[:Every nontrivial solution for
must be unbounded, provided , in and for every bounded subset I, f(t, z) is bounded in E × I.(B) Every bounded solution for , in , must be constant, provided in and for every bounded subset I, is bounded in .  相似文献   

5.
The concepts of an annihilator and a relative annihilator in an autometrized l-algebra are introduced. It is shown that every relative annihilator in a normal autometrized l-algebra is an ideal of and every principal ideal of is an annihilator of . The set of all annihilators of forms a complete lattice. The concept of an I-polar is introduced for every ideal I of . The set of all I-polars is a complete lattice which becomes a two-element chain provided I is prime. The I-polars are characterized as pseudocomplements in the lattice of all ideals of containing I.  相似文献   

6.
A transit function R on a set V is a function satisfying the axioms and , for all . The all-paths transit function of a connected graph is characterized by transit axioms.  相似文献   

7.
Let and be groups and let be an extension of by . Given a property of group compactifications, one can ask whether there exist compactifications and of N and K such that the universal -compactification of G is canonically isomorphic to an extension of by . We prove a theorem which gives necessary and sufficient conditions for this to occur for general properties and then apply this result to the almost periodic and weakly almost periodic compactifications of G.  相似文献   

8.
In this paper we investigate finite rank operators in the Jacobson radical of Alg( ), where are nests. Based on the concrete characterizations of rank one operators in Alg( ) and , we obtain that each finite rank operator in can be written as a finite sum of rank one operators in and the weak closure of equals Alg( ) if and only if at least one of is continuous.  相似文献   

9.
We prove that any infinite-dimensional non-archimedean Fréchet space E is homeomorphic to where D is a discrete space with card(D) = dens(E). It follows that infinite-dimensional non-archimedean Fréchet spaces E and F are homeomorphic if and only if dens(E) = dens(F). In particular, any infinite-dimensional non-archimedean Fréchet space of countable type over a field is homeomorphic to the non-archimedean Fréchet space .  相似文献   

10.
Let E be a real linear space. A vectorial inner product is a mapping from E×E into a real ordered vector space Y with the properties of a usual inner product. Here we consider Y to be a -regular Yosida space, that is a Dedekind complete Yosida space such that , where is the set of all hypermaximal bands in Y. In Theorem 2.1.1 we assert that any -regular Yosida space is Riesz isomorphic to the space B(A) of all bounded real-valued mappings on a certain set A. Next we prove Bessel Inequality and Parseval Identity for a vectorial inner product with range in the -regular and norm complete Yosida algebra .  相似文献   

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