Hyperspaces with a countable character of closed subsets

Hyperspaces of Closed Limit Sets

We study Michael’s lower semifinite topology and Fell’s topology on the collection of all closed limit subsets of a topological space. Special attention is given to the subfamily of all maximal limit sets.

SOME REMARKS ON GENERALIZATIONS OF MULTIPLICATIVELY CLOSED SUBSETS

Let R be a commutative ring with identity and Mbe a unitary R-module. In this paper we generalize the conceptmultiplicatively closed subset of R and we study some propertiesof these genaralized subsets of M. Among the many results in thispaper, we generalize some well-known theorems about multiplicativelyclosed subsets of R to these generalized subsets of M. Alsowe show that some other well-kno...

The Countable Character of Uncountable Graphs

We show that a graph can always be decomposed into edge-disjoint subgraphs of countable cardinality in which the edge-connectivities and edge-separations of the original graph are preserved up to countable cardinals. We also show that the vertex set of any graph can be endowed with a well-ordering which has a certain compactness property with respect to edge-separation.

The countable existentially closed pseudocomplemented semilattice

Remarks on Star Countable Discrete Closed Spaces

In this paper, we prove the following statements: (1) There exists a Tychonoff star countable discrete closed, pseudocompact space having a regular-closed subspace which is not star countable. (2) Every separable space can be embedded into an absolutely star countable discrete closed space as a closed subspace. (3) Assuming 20 = 21 , there exists a normal absolutely star countable discrete clos...