共查询到20条相似文献,搜索用时 15 毫秒
1.
Let X be an infinite set, C={G:G is a group defined on the X}, Define {H:H is isomorphic to G}, C_2={C & G js not commutative},then |C_2|=2 If K={F:F is a division ring defined on the X},K_1={K & F is not com mutative}, K_2={K & F is commutative},then |K_1| [ = IK2t --2:s~. Suppose T(X) {X~X & qψis bijective},S={G:G is a subgroup of T(X)},S_1={S & G is commutative}, S_2={S & G is not commutative},then |S_1|=|S_2|=2~(2~(|x|)). 相似文献
2.
Let X be an infinite set, C={B:B is a Boolean algebra defined on the X},Define B={D:D is isomorphie to B}, C={C & B is atomic},C_2= {C & B is not atomic},then |C_1|=|C_2|=2~(|x|). The power set of X is denoted by P(X), P(X) is a field of sets (Under Union and Intersection of sets, and Complement of set), Suppose K={F:F js a field of sets & FP(X)}, K_1={K},K_2{K & F is not atomie} then |K_1|=|K_2|=2~(2~(|x|)). 相似文献
3.
In this note we define a new topology on C(X),the set of all real-valued continuous functions on a Tychonoff space X.The new topology on C(X) is the topology having subbase open sets of both kinds:[f,C,ε[={g E C(X):|f(x)-g(x)| ε for every x∈C} and[U,r]~-={g∈C(X):g~(-1)(r)∩U≠φ},where f∈C(X),C∈KC(X)={nonempty compact subsets of X},ε 0,while U is an open subset of X and r∈R.The space C(X) equipped with the new topology T_(kh) which is stated above is denoted by C_(kh)(X).Denote X_0={x∈X:x is an isolated point of X} and X_c={x∈X:x has a compact neighborhood in X}.We show that if X is a Tychonoff space such that X_0=X_c,then the following statements are equivalent:(1) X_0 is G_δ-dense in X;(2) C_(kh)(X) is regular;(3) C_(kh)(X) is Tychonoff;(4) C_(kh)(X) is a topological group.We also show that if X is a Tychonoff space such that X_0=X_c and C_(kh)(X) is regular space with countable pseudocharacter,then X is σ-compact.If X is a metrizable hemicompact countable space,then C_(kh)(X) is first countable. 相似文献
4.
Let X be an infinite set, T(X)={f∈X~X:f is a bijection}, C={G:G is a transformation group on X}={G:G is a subgroup of T(X)}.Then |C|=2~(2~(|x|)). Inproof of this result, the AC is used. 相似文献
5.
Let X be an infinite set, K={τ:τ is a topology on X}, C={τ:τ∈K&τ is acomplete lattice of sets with respect to operations of arbitrary intersection andunion}. Theorem 1 For a given τ∈K, we define (τ)={σ:σ∈K & σo and τ are homeomorphic}, then sup{|<τ>):τ∈K}=max{|<τ>|:τ∈K}=2~|X|=exp(|X|). 相似文献
6.
The term (di)graph is employed to mean that a graph in question is either a directed graph or an undirected graph.The symbol G(p,r)represents the digraph defined by Chao: V(G(p,r))=Zp,E(G(p,r))={(x,y)|x-y∈Hr},where P is a prime,r is a positive divisor of P-1 and Hr is the unique subgroup of order r in Aut(Zp).A Cayley graph (?)=Cay(G,S)is called imprimitive if A=Aut((?))acts imprimitively on V((?)).Let (?)=Cay(G,S)be a connected imprimitive arc-transitive graph on G=Z×Z,B={B0,B1,…,Bp-1}the complete block system of A=Aut((?))on V((?))=G and K the kernel of A on B.Then obviously K≠1. 相似文献
7.
Let X be an infinite set, the power set of X is denoted by P(X). = {G:G and F are isomorphic in the sense of Boolean algebra}, C=(:F is an atomicsubfield in P(X)}. Define C_1(C) is an incomparable class if (_1,_2∈C_1)(F_1≠F_2→F_1 and F_2 are incomparable), then |C| = 2~2~(|x|)= max{|C_1|}. In proof of this result, the AC and GCH are used. The sense of "isomorphism" in [2] is understood as"φ(φ is a bejection on 相似文献
8.
Theorem 1 Let X be a nonempty countable set, K={: is a discrete metric space}, define ≌ iff((?)f) (f is an equilong isomorphism from to , for a given ∈K, define = { ∈K: ≌}. Let C={: ∈K},then |C|=|K|=|{d:d is a metric on X}|=2~((?)0) The Theorem 2 illustrates that there exists a nonempty countable set X on which we can define 2~((?)0) nondiscrete metric spaces such that they are not isomorphic each other. 相似文献
9.
Let K be a local field,that is.K is a locally compactnon-discrete complete and totally disconnected field.A non-Archimedean norm is endowed on K:x→|x|is a mapping from K intoR~+,such that(i)|X|=0 iff X=0;(ii)|xy|=|x||y|;(iii)|x+y|≤max{|x|,|y|}.Then|x|is called the absolute value of x.Theset={x∈K:|x|≤1}is the ring of integers in K,and={x∈K: 相似文献
10.
Define two extended real-valued functions l(x)and u(x)on X≡[0,1]subjectto the following restrictions: (i)-∞≤l(x)相似文献
11.
Li Wenxia 《数学物理学报(B辑英文版)》1999,19(2):214-219
Let C be the Cantor triadic set and let Cα=C+α={β+α: β∈C} for -1≤α≤ 1. Let Hp={α∈C: dim H(Cα∩C)=dim B(C α∩C)=(1-p)log 2/log 3}, 0< p< 1. The authors give the dimensions of C α∩C and Hp. In additionthe characteristic of Hp is described by means of some measure μ supported on C. 相似文献
12.
Let X be an infinite set,K={τ:τ is a topology on X},defineτ≌σ iff (f)(f is a lattice-isomorphism from τ to σ),for a given τ∈K we define τ={σ:σ∈K &σ≌τ}K(K)is an imcomparable class iff (τ∈K)(σ∈K)(τ≠→τ and σ are incomparable),M={K:K is an incomparable class}. Theorem 1 sup{|τ|:τ∈K}=max{|τ|:τ∈k}=|K|=2~2~[X]=exp(exp(|X|)). Theorem 2 sup{sup{|τ|:τ∈K}:KK & K is an incomparable class}=sup 相似文献
13.
A C*-system is a pair (B, G) consisting of a unital C*-algebra B and a continuous group homomorphism α: G → Aut(B) where G is a compact group and Aut(B) the group of automor-phisms of B. If K is a normal subgroup of G and BK = {B∈ B: k(B) = B, k ∈ K}, then BK is a G-invariant C*-subalgebra of B. On the other hand, if A is a G-invariant C*-algebra with BG A B, set G (A) = {g ∈ G: g(A) = A, A ∈ A}, G (A) is a normal subgroup of G. Clearly K G(BK) and we call K Galois closed ifK = G(BK). Similarly, A BG(A) and we call A Galois closed if A = BG(A). 相似文献
14.
谢淑翠 《纯粹数学与应用数学》1991,7(1):117-119
设 U={z:|z|<1},H={f:f在U内解析},B={f∈H:f(U)=U},B_0={f∈B:f(0)=0},S(f)={g∈H:g f}。α_1…,α_m是U内不同的复数。给定正整数K_1,K_2,…K_m满足 相似文献
15.
Assume that B is a compact subset on the real axis containing at least n+1 points,C(B) the normed linear space of all continuous functions defined on B,with Chebyshevnorm‖·‖,and G=span(g_1,…,g_n) an n-dimensional subspace of C(B).LetG_R={g=sum from j=1 to n a_jg_j:v(x)≤g(x)≤u(x),q_i≤sum from j=1 to n d_(ij)a_j≤p_i for i=1,…,l}where u,v are extended real-valued functions on B subject to -∞≤v(x)相似文献
16.
Lei YANG 《数学学报(英文版)》2022,(1)
Let X=G/Γbe a homogeneous space with ambient group G containing the group H=(SO(n,1))kand x∈X be such that Hx is dense in X.Given an analytic curve?:I=[a,b]→H,we will show that ifφsatisfies certain geometric condition,then for a typical diagonal subgroup A={a(t):t∈R}■H the translates{a(t)?(I)x:t>0}of the curve?(I)x will tend to be equidistributed in X as t→+∞.The proof is based on Ratner's theorem and linearization technique. 相似文献
17.
The (U + K)-orbit of a bounded linear operator T acting on a Hilbert space H is defined as (U + K)(T)={R-1 T R:R is invertible of the form unitary plus compact on H}.In this paper,we first characterize the closure of the (U + K)-orbit of an essentially normal triangular operator T satisfying H={ker(T-λI):λ∈ρ F (T)} and σ p (T*)=ф.After that,we establish certain essentially normal triangular operator models with the form of the direct sums of triangular operators,adjoint of triangular operators and normal operators,show that such operator models generate the same closed (U + K)-orbit if they have the same spectral picture,and describe the closures of the (U + K)-orbits of these operator models.These generalize some known results on the closures of (U + K)-orbits of essentially normal operators,and provide more positive cases to an open conjecture raised by Marcoux as Question 2 in his article "A survey of (U + K)-orbits". 相似文献
18.
Let ε:y2 =x3 + Ax + B be an elliptic curve defined over the finite field Zp(p > 3)and G be a rational point of prime order N on ε.Define a subset of ZN,the residue class ring modulo N,as S ∶={n ∶n ∈ZN,... 相似文献
19.
Highest weight representations of a Lie algebra of Block type 总被引:2,自引:0,他引:2
Yue-zhu WU & Yu-cai SU Department of Mathematics Shanghai Jiaotong University Shanghai China Department of Mathematics Qufu Normal University Qufu China Department of Mathematics University of Science Technology of China Hefei China 《中国科学A辑(英文版)》2007,50(4):549-560
For a field F of characteristic zero and an additive subgroup G of F, a Lie algebra B(G) of the Block type is defined with the basis {Lα,i, c|α∈G, -1≤i∈Z} and the relations [Lα,i,Lβ,j] = ((i 1)β- (j 1)α)Lα β,i j αδα,-βδi j,-2c,[c, Lα,i] = 0. Given a total order (?) on G compatible with its group structure, and anyα∈B(G)0*, a Verma B(G)-module M(A, (?)) is defined, and the irreducibility of M(A,(?)) is completely determined. Furthermore, it is proved that an irreducible highest weight B(Z )-module is quasifinite if and only if it is a proper quotient of a Verma module. 相似文献
20.
PARTITION A GRAPH WITH SMALL DIAMETER INTO TWO INDUCED MATCHINGS 总被引:5,自引:0,他引:5
Yang Aifeng Yuan Jinjiang Dept. of Appl. Math. South China Univ. of Tech. Guangdong China. Dept. of Math. Zhengzhou Univ. Henan China. 《高校应用数学学报(英文版)》2004,19(3):245-251
§1 IntroductionGraphs considered in this paper are finite and simple.For a graph G,its vertex setandedge set are denoted by V(G) and E(G) ,respectively.If vertices u and v are connected inG,the distance between u and v,denoted by d G(u,v) ,is the length ofa shortest(u,v) -pathin G.The diameter of a connected graph G is the maximum distance between two verticesof G.For X V(G) ,the neighbor set NG(X) of X is defined byNG(X) ={ y∈V(G) \X:there is x∈X such thatxy∈E(G) } .NG({ x} )… 相似文献