In this work, we present new types of compact and Lindelöf spaces and  some facts and results related to them. There are also types of compact and Lindelöf functions and the relationship between them has been investigated. Further, we have present some properties and results related to them.

This research deals with deliberative intentionality in its two dimensions, deliberative intent, direct, and indirect deliberative intent, and deliberative intentionality assumed great importance to ancient and contemporary scholars. The text, relying on deliberative intent as a methodology concerned with the study of language in usage, and the research focuses on direct deliberative intent through (the intent of acceptability, the intent of the presumption, the intent of the informational, the intent of interaction), and the indirect deliberative intent through (the intentionality of the case, the intent of the metaphor, The intent of the communicative impulse, the intent of the allusion,), and these deliberative elements activate and c

    The aim of our work is to develop a new type of games which are related to (D, WD, LD) compactness of topological groups. We used an infinite game that corresponds to our work. Also, we used an alternating game in which the response of the second player depends on the choice of the first one. Many results of winning and losing strategies have been studied, consistent with the nature of the topological groups. As well as, we presented some topological groups, which fail to have winning strategies and we give some illustrated examples. Finally, the effect of functions on the aforementioned compactness strategies was studied.  

In this paper, we provide some types of - -spaces, namely, - ( )- (respectively, - ( )- , - ( )- and - ( )-) spaces for minimal structure spaces which are denoted by ( -spaces). Some properties and examples are given.
The relationships between a number of types of - -spaces and the other existing types of weaker and stronger forms of -spaces are investigated. Finally, new types of open (respectively, closed) functions of -spaces are introduced and some of their properties are studied.

    In this paper, some new types of regularity axioms, namely pairwise quasi-regular, pairwise semi-regular, pairwise pseudo regular and pairwise regular are defined and studied in both ech fuzzy soft bi-closure spaces (  bicsp’s) and their induced fuzzy soft bitopological spaces. We also study the relationships between them. We show that in all these types of axioms, the hereditary property is satisfied under closed fs bi-csubsp of . Furthermore, we define some normality axioms, namely pairwise semi-normal, pairwise pseudo normal, pairwise normal and pairwise completely normal in both  bicsp’s and their induced fuzzy soft bitopological spaces, as well as their basic properties and the relationships between them are studied.

In this paper, we define a new type of pairwise separation axioms called pairwise semi-p- separation axioms in bitopological spaces, also we study some properties of these spaces and relationships of each one with the ordinary separation axioms in the bitopological spaces.

The main purpose of this paper, is to introduce a topological space , which is induced by reflexive graph and tolerance graph , such that  may be infinite. Furthermore, we offered some properties of  such as connectedness, compactness, Lindelöf and separate properties. We also study the concept of approximation spaces and get the sufficient and necessary condition that topological space is approximation spaces.

This paper focuses on developing a strategy to represent the -connected ominoes using an abacus. We use the idea of -connected ominoes with respect to a frame in modelling nested chain abacus. Then, we formulate and prove the unique connected partition for any -connected ominoes. Next, the topological structure of nested chain abacus is presented.

Here, we found an estimation of best approximation of unbounded functions which satisfied weighted Lipschitz condition with respect to convex polynomial by means of weighted Totik-Ditzian modulus of continuity

In this paper we define and study new concepts of fibrewise topological spaces over B namely, fibrewise near compact and fibrewise locally near compact spaces, which are generalizations of well-known concepts near compact and locally near compact topological spaces. Moreover, we study relationships between fibrewise near compact (resp., fibrewise locally near compact) spaces and some fibrewise near separation axioms.