On normality of a closure space generated from a tree by relation

Binary relation plays a prominent role in the study of mathematics in particular applied mathematics. Recently, some authors generated closure spaces through relation and made a comparative study of topological properties in the space by varying the property on the relation. In this paper, we have studied closure spaces generated from a tree through binary relation and observed that under certain situation the space generated from a tree is normal.

Representation of bifinite domains by BF-closure spaces

In this paper, we propose the notion of BF-closure spaces as concrete representation of bifinite domains. We prove that every bifinite domain can be obtained as the set of F-closed sets of some BF-closure space under set inclusion. Furthermore, we obtain that the category of bifinite domains and Scott-continuous functions is equivalent to that of BF-closure spaces and F-morphisms.

Some Variants of Normal Čech Closure Spaces via Canonically Closed Sets

New generalizations of normality in Čech closure space such as π-normal, weakly π-normal and κ-normal are introduced and studied using canonically closed sets. It is observed that the class of κ-normal spaces contains both the classes of weakly π-normal and almost normal Čech closure spaces.

C̆ech Fuzzy Soft Closure Spaces

In this paper, the C̆ech fuzzy soft closure spaces are defined and their basic properties are studied. Closed (respectively, open) fuzzy soft sets is defined in C̆ech fuzzy-soft closure spaces. It has been shown that for each C̆ech fuzzy soft closure space there is an associated fuzzy soft topological space. In addition, the concepts of a subspace and a sum are defined in C̆ech fuzzy soft closure space. Finally, fuzzy soft continuous (respectively, open and closed) mapping between C̆ech fuzzy soft closure spaces are introduced. Mathematics Subject Classification: 54A40, 54B05, 54C05.

Group of closure isomorphisms of Cech closure spaces

Here we discuss some results on the group of all closure isomorphisms of a \u{C}ech closure space. A subgroup \(H\) of the symmetric group \(S(X)\) is \(c\) representable on $X$ if there exists a closure operator \(V\) on $X$ such that the group of closure isomorphisms of the closure space \((X,\ V)\) is \(H\). In this paper, we prove a non trivial normal subgroup of the symmetric group \(S(X)\) is \(c\)-representable on \(X\) if and only if the cardinality of \(X\) is three.