Abstract In topological modal logic, it is well known that the Cantor derivative more expressive than closure, and ‘elsewhere’, or ‘difference’, operator ‘somewhere’ operator. 2014, Kudinov Shehtman asked whether combination of closure elsewhere becomes strictly when adding derivative. this paper we give an affirmative answer: in fact, alone can define properties spaces not expressible with els...

This paper dualizes the setting of affine spaces as originally introduced by Diers for application to algebraic geometry and expanded upon by various authors, to show that the fundamental groups of pointed topological spaces appear as the structures of dually affine spaces. The dual of the Zariski closure operator is introduced, and the 1-sphere and its copowers together with their fundamental ...

This paper is devoted to the study of nondeterministic closure automata, that is, nondeterministic finite automata (nfas) equipped with a strict closure operator on the set of states and continuous transition structure. We prove that for each regular language L there is a unique minimal nondeterministic closure automaton whose underlying nfa accepts L. Here minimality means no proper sub or quo...

the main goal of this paper is to introduce and study a new class of function via the notions of $e$-$theta$-open sets and $e$-$theta$-closure operator which are defined by özkoç and aslım cite{10} called weakly $er$-open functions and $e$-$theta$-open functions. moreover, we investigate not only some of their basic properties but also their relationships with other types of already existing to...

In belief revision, the result of a contraction should be a logically closed set (closure) such that the input is not inferred (success). Traditionally, these two postulates depend on the same consequence operator. The present work investigates the consequences of using two different consequence operators for each of these desiderata: the classic Cn to compute success and a second weaker operat...

1.1 What is a Group? A group is a set of objects with an associated operation which satisfies certain properties. For a group G which is a set of elements {T, T ′, T ′′, ...} with operator ◦, we require: 1. Closure. ∀T, T ′ ∈ G : T ◦ T ′ ∈ G. This property of closure should be familiar to anyone with a linear algebra background, as a vector space also fulfills this property, with addition as th...

The generalised structural arrangements of various bimolecule such as carbohydrates, proteins etc are based on the rules ofČech closure operator. In this paper we discuss the relationship betweeň Cech closure space and structural configuration of proteins.

We argue that closure operators are fundamental tools for the study of relationships between order structures and their sequence representations. We also propose and analyse a closure operator for interval order structures.

There are many symmetries in intuitionistic fuzzifying topology. In the present paper, notion of topology as an extension and a preliminary research on bi-intuitionistic fuzzy is introduced. A theory with semantic method logic established.