The notion of contra continuous functions was introduced and investigated by Dontchev. In this paper, we apply the notion of $beta^{*}$-closed sets in topological space to present and study a new class of functions called contra $beta^{*}$-continuous and almost contra $beta^{*}$-continuous functions as a new generalization of contra continuity.

Session 1. 8:40 10:15 AM. Melamed Benjamin Rutgers University, Chair Berge’s Maximum Theorem for Non-compact Image Sets and Its Applications. Pavlo Kasyanov, Kyiv Polytechnic Institute & World Data Center, Ukraine and Eugene A. Feinberg, Stony Brook University. For an upper semi-continuous set-valued mapping from one topological space to another and for a lower semi-continuous function defined ...

we shall give a lower estimate of harmonic‎ ‎functions of order greater than one in a half space‎, ‎which‎ ‎generalize the result obtained by b‎. ‎ya‎. ‎levin in a half plane‎.

Azad [1] introduced the concepts of fuzzy semi-open sets and fuzzy semi-continuous mappings. Fuzzy α-open sets and fuzzy α-continuous functions were introduced by Mashhour et. al. [4] and Singal et. al. [6] respectively. The concepts of fuzzy pre-open sets and fuzzy pre-continuous mappings were introduced by Bin Sahana [2]. In this paper the concepts of fuzzy α-quotient maps, fuzzy semi quotien...

In this paper, we extend the notions of γ-operation introduced in [12], by using the soft ideal notions. We introduce the notions of Ĩ-open soft sets, pre-Ĩopen soft sets, α-Ĩ-open soft sets, semi-Ĩ-open soft sets and β-Ĩ-open soft sets to soft topological spaces. We study the relations between these different types of subsets of soft topological spaces with soft ideal. We also introduce the co...

In this paper, we introduce the notions of fuzzy γ-I-open sets and fuzzy γ-I-continuous functions to obtain a decomposition of fuzzy semi-I-continuity. We also investigated the fundamental properties of such functions.

A metric defined by Fine induces a topology on the unit interval which is strictly stronger than the ordinary Euclidean topology and which has some interesting applications in Walsh analysis. We investigate computability properties of a corresponding Fine representation of the real numbers and we construct a structure which characterizes this representation. Moreover, we introduce a general cla...

The concept of a preopen set in a topological space was introduced by H. H. Corson and E. Michael in 1964 [3]. A subset A of a topological space (X, τ) is called preopen or locally dense or nearly open if A ⊆ Int(Cl(A)). A set A is called preclosed if its complement is preopen or equivalently if Cl(Int(A)) ⊆ A. The term, preopen, was used for the first time by A. S. Mashhour, M. E. Abd El-Monse...