In point set topology, it is well known that the Kuratowski 14-set problem is one of the most interesting results. In this note, we first give a brief survey of the Kuratowski’s theorem. In particular, we will study ...In point set topology, it is well known that the Kuratowski 14-set problem is one of the most interesting results. In this note, we first give a brief survey of the Kuratowski’s theorem. In particular, we will study and investigate the structure of the boundary of a given subset in a topological space. Some new results and topics which are related to the theorem of Kuratowski are presented and discussed. Finally, we pose some open problems of Kuratowskitype.展开更多
We describe the relationship between the fuzzy sets and the algebraic hyperstructures. In fact, this paper is a continuation of the ideas presented by Davvaz in （Fuzzy Sets Syst., 117： 477- 484, 2001） and Bhakat an...We describe the relationship between the fuzzy sets and the algebraic hyperstructures. In fact, this paper is a continuation of the ideas presented by Davvaz in （Fuzzy Sets Syst., 117： 477- 484, 2001） and Bhakat and Das in （Fuzzy Sets Syst., 80： 359-368, 1996）. The concept of the quasicoincidence of a fuzzy interval value with an interval-valued fuzzy set is introduced and this is a natural generalization of the quasi-coincidence of a fuzzy point in fuzzy sets. By using this new idea, the concept of interval-valued （α,β）-fuzzy sub-hypermodules of a hypermodule is defined. This newly defined interval-valued （α,β）-fuzzy sub-hypermodule is a We shall study such fuzzy sub-hypermodules and sub-hypermodules of a hypermodule. generalization of the usual fuzzy sub-hypermodule. consider the implication-based interval-valued fuzzy展开更多
In this paper, we study the class of ortho-u-monoids which are generalized orthogroups within the class of E（S）-semiabundant semigroups. After introducing the concept of （-）-Green＇s relations, and obtaining some ...In this paper, we study the class of ortho-u-monoids which are generalized orthogroups within the class of E（S）-semiabundant semigroups. After introducing the concept of （-）-Green＇s relations, and obtaining some important properties of （-）-Green＇s relations and super E（S）-semiabundant semigroups, we have given the semilattice decomposition of ortho-u-monoids and a structure theorem for regular ortho-u-monoids. The main techniques that we used in the study are the （-）-Green＇s relations, and the semi-spined product of semigroups.展开更多
文摘In point set topology, it is well known that the Kuratowski 14-set problem is one of the most interesting results. In this note, we first give a brief survey of the Kuratowski’s theorem. In particular, we will study and investigate the structure of the boundary of a given subset in a topological space. Some new results and topics which are related to the theorem of Kuratowski are presented and discussed. Finally, we pose some open problems of Kuratowskitype.
基金the National Natural Science Foundation of China(60474022)the Key Science Foundation of Education Commission of Hubei Province, China (D200729003+1 种基金D200529001)the research of the third author is partially supported by an RGC grant (CUHK) #2060297(05/07)
文摘We describe the relationship between the fuzzy sets and the algebraic hyperstructures. In fact, this paper is a continuation of the ideas presented by Davvaz in （Fuzzy Sets Syst., 117： 477- 484, 2001） and Bhakat and Das in （Fuzzy Sets Syst., 80： 359-368, 1996）. The concept of the quasicoincidence of a fuzzy interval value with an interval-valued fuzzy set is introduced and this is a natural generalization of the quasi-coincidence of a fuzzy point in fuzzy sets. By using this new idea, the concept of interval-valued （α,β）-fuzzy sub-hypermodules of a hypermodule is defined. This newly defined interval-valued （α,β）-fuzzy sub-hypermodule is a We shall study such fuzzy sub-hypermodules and sub-hypermodules of a hypermodule. generalization of the usual fuzzy sub-hypermodule. consider the implication-based interval-valued fuzzy
基金Supported by National Natural Science Foundation of China （Grant Nos. 10871161, 10926031）, Natural Science Foundation Project of CQ CSTC2009BB2291, the Young Science and Technology Fund of Xi＇an University of Architecture and Technology （Grant No. QN0829）
文摘In this paper, we study the class of ortho-u-monoids which are generalized orthogroups within the class of E（S）-semiabundant semigroups. After introducing the concept of （-）-Green＇s relations, and obtaining some important properties of （-）-Green＇s relations and super E（S）-semiabundant semigroups, we have given the semilattice decomposition of ortho-u-monoids and a structure theorem for regular ortho-u-monoids. The main techniques that we used in the study are the （-）-Green＇s relations, and the semi-spined product of semigroups.
