By investigating the properties of Hellinger-Toeplitz topologies, we establish a general version of Kalton's cioed graph theorem. From this general version, we deduce a number of new closed graph theorems, which a...By investigating the properties of Hellinger-Toeplitz topologies, we establish a general version of Kalton's cioed graph theorem. From this general version, we deduce a number of new closed graph theorems, which are convenient for application. Particularly we improve some results of Kalton.展开更多
By introducing the notions of L-spaces and L_r-spaces, a complete generalization of Kalton's closed graph theorem is obtained. It points out the class of L_r-spaces is the maximal class of range spaces for the clo...By introducing the notions of L-spaces and L_r-spaces, a complete generalization of Kalton's closed graph theorem is obtained. It points out the class of L_r-spaces is the maximal class of range spaces for the closed graph theorem when the class of domain spaces is the class of Mackey spaces with weakly * sequentially complete dual.Some examples are constructed showing that the class of L_r-spaces is strictly larger than the class of separable B_r-complete spaces.Some properties of L-spaces and L_r-spaces are discussed and the relations between B-complete (resp. B_r-complete) spaces and L-spaces (resp. L_r-spaces) are given.展开更多
The aim of this paper is to redefine upper semicotinuous,lower semicotinuous and continuous correspondences on super spaces,which are improvement of Klein′s Definition 7.1.1 in .Some characterizations and properties...The aim of this paper is to redefine upper semicotinuous,lower semicotinuous and continuous correspondences on super spaces,which are improvement of Klein′s Definition 7.1.1 in .Some characterizations and properties of these correspondences and their closed graph are obtained,applications of subsets nets in lower semicontinuous correspondence are given.展开更多
In this paper, we give some new results of the coefficient multiplier of some analytic function spaces, characterize the coefficient multiplier spaces (Hα, p Hβ q) and (Ap,α), Aq,β) with 0 < p ≤ 1, p ≤ q ≤∞...In this paper, we give some new results of the coefficient multiplier of some analytic function spaces, characterize the coefficient multiplier spaces (Hα, p Hβ q) and (Ap,α), Aq,β) with 0 < p ≤ 1, p ≤ q ≤∞, 0 ≤α < β < ∞ and show (Hα∞, Hβ∞) = Hβ-α1 with 0 < α < β < ∞.展开更多
For a convex set-valued map between p-normed (0 < p < 1) spaces, we give a criterion for its inverse to be locally Lipschitz of order p. From this we obtain the Robinson-Ursescu Theorem in p-normed spaces and th...For a convex set-valued map between p-normed (0 < p < 1) spaces, we give a criterion for its inverse to be locally Lipschitz of order p. From this we obtain the Robinson-Ursescu Theorem in p-normed spaces and the open mapping and closed graph theorems for closed convex set-valued maps.展开更多
Let CCM denote the class of closed graphs with Cohen-Macaulay binomial edge ideals and PIG denote the class of proper interval graphs.Then CCM⊆PIG The PIG-completion problem is a classical problem in graph theory as w...Let CCM denote the class of closed graphs with Cohen-Macaulay binomial edge ideals and PIG denote the class of proper interval graphs.Then CCM⊆PIG The PIG-completion problem is a classical problem in graph theory as well as in molecular biology,and this problem is known to be NP-hard.In this paper,we study the CCM-completion problem.We give a method to construct all possible CCM-completions of a graph.We find the CCM-completion number and the set of all minimal CCM-completions for a large class of graphs.Moreover,for this class,we give a polynomial-time algorithm to compute the CCM-completion number and a minimum CCM-completion of a given graph.The unmixedness and Cohen-Macaulay properties of binomial edge ideals of induced subgraphs are investigated.Also,we discuss the accessible graph completion and the Cohen-Macaulay property of binomial edge ideals of whisker graphs.展开更多
A graph G is close to regular or more precisely a （d, d ＋ k）-graph, if the degree of each vertex of G is between d and d ＋ k. Let d ≥ 2 be an integer, and let G be a connected bipartite （d, d＋k）-graph with par...A graph G is close to regular or more precisely a （d, d ＋ k）-graph, if the degree of each vertex of G is between d and d ＋ k. Let d ≥ 2 be an integer, and let G be a connected bipartite （d, d＋k）-graph with partite sets X and Y such that ｜X｜- ｜Y｜＋1. If G is of order n without an almost perfect matching, then we show in this paper that·n ≥ 6d ＋7 when k = 1,·n ≥ 4d＋ 5 when k = 2,·n ≥ 4d＋3 when k≥3.Examples will demonstrate that the given bounds on the order of G are the best possible.展开更多
文摘By investigating the properties of Hellinger-Toeplitz topologies, we establish a general version of Kalton's cioed graph theorem. From this general version, we deduce a number of new closed graph theorems, which are convenient for application. Particularly we improve some results of Kalton.
文摘By introducing the notions of L-spaces and L_r-spaces, a complete generalization of Kalton's closed graph theorem is obtained. It points out the class of L_r-spaces is the maximal class of range spaces for the closed graph theorem when the class of domain spaces is the class of Mackey spaces with weakly * sequentially complete dual.Some examples are constructed showing that the class of L_r-spaces is strictly larger than the class of separable B_r-complete spaces.Some properties of L-spaces and L_r-spaces are discussed and the relations between B-complete (resp. B_r-complete) spaces and L-spaces (resp. L_r-spaces) are given.
文摘The aim of this paper is to redefine upper semicotinuous,lower semicotinuous and continuous correspondences on super spaces,which are improvement of Klein′s Definition 7.1.1 in .Some characterizations and properties of these correspondences and their closed graph are obtained,applications of subsets nets in lower semicontinuous correspondence are given.
文摘In this paper, we give some new results of the coefficient multiplier of some analytic function spaces, characterize the coefficient multiplier spaces (Hα, p Hβ q) and (Ap,α), Aq,β) with 0 < p ≤ 1, p ≤ q ≤∞, 0 ≤α < β < ∞ and show (Hα∞, Hβ∞) = Hβ-α1 with 0 < α < β < ∞.
基金The NSF (Q1107107) of Jiangsu Educational Commission.
文摘For a convex set-valued map between p-normed (0 < p < 1) spaces, we give a criterion for its inverse to be locally Lipschitz of order p. From this we obtain the Robinson-Ursescu Theorem in p-normed spaces and the open mapping and closed graph theorems for closed convex set-valued maps.
文摘Let CCM denote the class of closed graphs with Cohen-Macaulay binomial edge ideals and PIG denote the class of proper interval graphs.Then CCM⊆PIG The PIG-completion problem is a classical problem in graph theory as well as in molecular biology,and this problem is known to be NP-hard.In this paper,we study the CCM-completion problem.We give a method to construct all possible CCM-completions of a graph.We find the CCM-completion number and the set of all minimal CCM-completions for a large class of graphs.Moreover,for this class,we give a polynomial-time algorithm to compute the CCM-completion number and a minimum CCM-completion of a given graph.The unmixedness and Cohen-Macaulay properties of binomial edge ideals of induced subgraphs are investigated.Also,we discuss the accessible graph completion and the Cohen-Macaulay property of binomial edge ideals of whisker graphs.
文摘A graph G is close to regular or more precisely a （d, d ＋ k）-graph, if the degree of each vertex of G is between d and d ＋ k. Let d ≥ 2 be an integer, and let G be a connected bipartite （d, d＋k）-graph with partite sets X and Y such that ｜X｜- ｜Y｜＋1. If G is of order n without an almost perfect matching, then we show in this paper that·n ≥ 6d ＋7 when k = 1,·n ≥ 4d＋ 5 when k = 2,·n ≥ 4d＋3 when k≥3.Examples will demonstrate that the given bounds on the order of G are the best possible.
