On real valued ω-continuous functions

2012

The aim of this paper is to introduce a new class of continuous multifunctions, namely upper and lower ω̂-continuous multifunctions and to obtain some characterizations concerning upper and lower ω̂continuous multifunctions. Mathematics Subject Classification: 57C05

Cubo (Temuco), 2017

In this paper, we apply the notion of ω-open sets due to Arhangel'skiȋ to present and study a new class of functions called almost ω-continuous functions. Relationships between this new class and other classes of functions are established. En este artículo, aplicamos la noción de ω-conjuntos abiertos dada por Arhangel'skiȋ [1] para presentar y estudiar una nueva clase de funciones llamadas funciones casi ωcontinuas. Establecemos relaciones entre esta nueva clase y otras clases de funciones.

Tatra Mountains Mathematical Publications, 2009

In the present paper, we introduce the notion of classes of ρ-upper continuous functions. We show that ρ-upper continuous functions are Lebesgue measurable and, for ρ < 1/2 , may not belong to Baire class 1. We also prove that a function with Denjoy property can be non-measurable.

The main purpose of this paper is to study ωe *-continuity via ωe *-open sets. We obtain several characterizations and some fundamental properties of ωe *continuous functions. Also, we introduce some new functions such as ωe *-irresolute functions, ωe *-open functions and ωe *-closed functions by means of ωe *-open sets. Moreover, we obtain that ωe *-open function is independent with ωe *-irresolute function and ωe *-continuous function. Furthermore, we give not only various properties and characterizations but also examples and counterexamples.

Journal of Advanced Studies in Topology, 2013

In [1], the authors introduced and studied the notion of almost ωcontinuity in topological spaces. In this paper, we investigate some more properties of this type of continuity.

Journal of Southwest Jiaotong University

The aim of this paper is to add new types of continuous functions and results in the specialization field, where we merge two important terms of open sets that are pre-open and ω-open to get a new set named ωp-open set, where we introduce new functions by using this set, such as Mωpc, ωpMc, ωpMωpc, ωp-continuous, ωp*-continuous, and ωp-irresolute function. We clarify the relationship between these types and illustrate their relationship with some other types of continuous functions. Also we define some new types of spaces such as, ωp-compact, ωp-Lindelöf, and Cωp-Lindelöf. In addition, we submit important results like, the ωp*-continuous image of compact space being ωp-compact, and if X is a ωp-regular space, hence it is Cωp-Lindelöf, as well as we provide the composition between most of the new functions that we defined. Many other results have been found in this our work and they are supported by many examples.

On sub weakly w continuous functions, 2018

The purpose of this paper is to introduce a new class functions called, sub weakly ω-continuous functions. Also, we obtain its characterizations and its basic properties.

International Journal of Mathematics and …

The notion of contra continuous functions was introduced and investigated by Dontchev. In this paper, we apply the notion of ω-open sets in topological space to present and study a new class of functions called almost contra ω-continuous functions as a new generalization of contra ...

Annals of the University of Craiova - Mathematics and Computer Science Series, 2010

In [5], Hdeib introduced and investigated a new type of continuity called ω -continuity. In [1], Al-Omari and Noorani have introduced the notion of almost weak ω -continuity. It is the objective of this paper to study almost weak ω -continuity and present some of its basic properties.

2014

The purpose of this paper is to introduce and study a new generalization of ω-continuous multifunction called slightly ω-continuous multifunctions in topological spaces. AMS (MOS) Subject Classification Codes: 54C10, 54C08, 54C05