关于子基的连通性

覆盖方法在粗糙集理论研究中的应用越来越受到重视,而其中最重要的两个概念是最近引入的拓扑空间的子集关于子基的内部和闭包.本文研究由它们导出的关于子基的连通性的概念,它比一般拓扑学中的连通性的概念弱,但具有许多类似的性质,这些性质事实上也是连通性相应结果的推广.     

无限维空间拟凸映射多目标最优化问题解集的连通性

本文在一个无限格中引入了拟凸、强拟凸和严格拟凸映射。并在约束集为紧凸条件下，证明了相应的多目标规划问题之有效解集和弱有效解集连通性结果。     

Connectedness of Kronecker sum and partial Kronecker row sum of designs

In this paper we discuss connectedness of a design which is a Kronecker sum or a partial Kronecker row sum of any two equi-replicate and equi-block size designs.     

A note on generalized connectedness

This note is devoted to study the preservation of connectedness under the basic operators in generalized topological spaces. Some characterizations of generalized connectedness are given. As an application, we generalize some results in topological spaces. Supported in part by the NSFC (No. 10571151, 10671173).     

Cohomological dimension of certain algebraic varieties

Let be an ideal of a commutative Noetherian ring . For finitely generated -modules and with , it is shown that . Let be a finitely generated module over a local ring such that . Using the above result and the notion of connectedness dimension, it is proved that Here denotes the connectedness dimension of the topological space . Finally, as a consequence of this inequality, two previously known generalizations of Faltings' connectedness theorem are improved.

     

Efficient Sets of Convex Compacta are Arcwise Connected

We prove that the efficient point set Max(Q|K) of a compact convex set QX in a Hausdorff topological vector space X ordered by a closed convex pointed cone KX with nonempty K ⁺ⁱ:={lK\{0}:l(x)>0} is arcwise connected.     

Counting Cocomponents of a Topological Space

Dualizing the statement about a number of components of a topological space X, we say that, for a natural number n, the space X has at most n cocomponents if every continuous map f:X ⁿ⁺¹X factorizes through X ⁿ , i.e., f depends on at most n coordinates. We construct metrizable spaces X ₁,X ₂,X ₃ such that(1) X ₁ does not have finitely many cocomponents but every continuous map X ₁ X ₁ depends only on finitely many coordinates;(2) X ₂=A×B for rigid spaces A,B and there is a continuous map X ₂ X ₂ depending on all coordinates;(3) X ₃(n) has precisely n cocomponents but it cannot be expressed as A×B with |A|>1 and |B|>1.     

On a representation of monounary algebras

In this note we deal with a question concerning monounary algebras which is analogous to an open problem for partially ordered sets proposed by Duffus and Rival.Support of Slovak VEGA Grant 1/7468/20 is acknowledged.     

Combinatorial Continuity in Complex Polynomial Dynamics

We describe how polynomials with all cycles repelling and connectedJulia set are organized in the boundary of the shift loci accordingto their real laminations. 2000 Mathematics Subject Classification37F20, 37F45.