This paper provides a method for combining interval structures. This method consists of three steps: it rst uses the product space to represent the new evidence space, then composes the cylindrical extensions of the interval structures on subspaces respectively , and nally combines the cylindrical extensions on the same product space. On the other hand, in order to interpret the method for comb...

We shall show that the union-closed families conjecture holds for a random union-closed family with high probability. This strengthens a recent result of Bruhn and Schaudt.

This course introduces main concepts from the theory of random sets with emphasis on applications in economics and finance: most importantly inference for partially identified models and transaction costs modelling. The main mathematical ideas introduced in this course are that of a random closed set, its distribution and main analytical tools to handle it, selections and expectations of random...

Let [n]:={1,2,…,n} and let a k-set denote set of cardinality k. A family sets is union-closed (UC) if the union any two in also family. Frankl’s conjecture states that for nonempty UC F⊆2[n] such F≠{∅}, there exists an element i∈[n] contained at least half F, where 2[n] denotes power on [n]. The 3-sets Morris smallest number distinct (whose n-set) ensure satisfied (in contains them ⌊n/2⌋+1 all ...

This study introduce a new type of closed sets in topology called Generalized h-closed (briefly, gh-closed) define as follow: E ⊆ χ be gh-closed set if CLh (E)⊆ U whenever and is open (χ,τ). The relation between other classes ( h-closed, g-closed, g -closed, g-closed αg-closed) are studied. Also, the notion gh-continuous mapping on topological space some properties proved. Finally, separation a...

In this paper we have introduced a new class of closed in topological spaces called g**-closed sets and study some its properties . Further introduce the concept g**-continuous functions , g**-irresolute As an application two news paces namely T **-space, **T - space .Further, g**-continuous, mappings are also investigated