Ali A. Atoom

Independent Researcher

This study investigates emerging concepts for defining and categorizing topological spaces based on various features. Paralindelöf spaces are one such idea that is required to understand the compactness and covering features of topological spaces. This study is the first to introduce D-paralindelöf spaces, a novel type of topological space defined...

An interesting area of research in topology is $D-$paracompact spaces. It is a significant type of topological spaces that retain compactness while benefiting from paracompactness, which it is considerd as generalisation of compact spaces. The concept of $D-$paracompactness was introduced and its basic characteristics were examined by the author in...

An interesting area of research in topology is D−paracompact spaces. It is a significant type of topological spaces that retain compactness while benefiting from paracompactness, which is considered a generalisation of compact spaces. The concept of D−paracompactness was introduced, and its basic characteristics were examined by the author in [18]....

An interesting area of research in topology is D−paracompact spaces. It is a significant type of topological spaces that retain compactness while benefiting from paracompactness, which is considered a generalisation of compact spaces. The concept of D−paracompactness was introduced, and its basic characteristics were examined by the author in [18]....

Many studies have employed a variety of techniques to further investigate topological space, particularly the notion of bitopological spaces, due to the significance of topological space in data processing as well as certain implementations. Numerous extended topological structures have been laid out subsequently. Of those abstractions, functions i...

In the present study, we introduce the notion of properly closed hereditary qualities in topological spaces. We discuss whether precompact, metacompact, and-spaces display the correctly closed hereditary character. By providing definitive answers to these queries and introducing characterizations of these spaces, a contribution to a deeper comprehe...

In this paper, the concept of D−sets will be applied to create D−lindelöf spaces, a new type of topological space covering the property. This is performed by using a D−cover, which is a special type of cover. The primary purpose of this work is to introduce the principles and concepts of D−lindelöf spaces. We look into their properties as well as t...

A topological space $ \left(X, \tau \right) $ is called a $ KC $-space when every compact subset of $ X $ is closed. The aim of this paper is to introduce new, namely $ KC $-bitopological spaces and pairwise $ KC $-topological spaces "$ P $-$ KC $-topological spaces". We examined the properties of these concepts and showed the relationships between...

The continuity is generalized by the notion of ω-continuous functions. In this research, we present a new weaker form for continuous functions called pairwise ω-continuous functions. Additionally, we define pairwise barely ω-continuous functions, a new, weaker form of barely ω-continuous functions. We study the basic characteristics and impacts of...

Topology

This paper defines new covering properties in tri-topological spaces called tri-Lindelöf space and the properties of this topological property and its relationship with some other types of tri-topological spaces will be studied. The effect of some types of functions on tri-Lindelöf spaces will be studied. This paper also investigates the necessary...

Everyday problems are characterized by voluminous data and varying levels of ambiguity. Thereupon, it is critical to develop new mathematical approaches to dealing with them. In this context, the perfect functions are anticipated to be the best instrument for this purpose. Therefore, we investigate in this paper how to generate perfect functions us...

In this article, we will present a new form of functions called pairwise􀀀 w- perfect functions and pairwise M-w-perfect functions. We will give some properties of this functions, and we will looking for homeomorphism of different bitopological spaces under the effect these functions. Last but not least, we give the characterizations of product theo...

In this paper we introduce the notions and concepts of the perfect functions in the bitopological spaces, 9 which yield to two types called p-lindelö perfect and s-lindelö perfect function. Also we study the images and 10 inverse images of certain bitopological properties under these functions.We derive some related results. Finally 11 some product...

In [9] the author, introduce the notion of ω-compactness and investigated its fundamental properties. In this paper we introduce and study a pairwise ω-compact spaces in bitopological spaces, and we investigate some more properties of this type of compact spaces.