The purpose of this paper is to introduce a new type of compact spaces, namely semi-p-compact spaces which are stronger than compact spaces; we give properties and characterizations of semi-p-compact spaces.

We define and study new ideas of fibrewise topological space on D namely fibrewise multi-topological space on D. We also submit the relevance of fibrewise closed and open topological space on D. Also fibrewise multi-locally sliceable and fibrewise multi-locally section able multi-topological space on D. Furthermore, we propose and prove a number of statements about these ideas.

            This work, introduces some concepts in bitopological spaces, which are nm-j-ω-converges to a subset, nm-j-ω-directed toward a set, nm-j-ω-closed mappings, nm-j-ω-rigid set, and nm-j-ω-continuous mappings. The mainline idea in this paper is nm-j-ω-perfect mappings in bitopological spaces such that n = 1,2  and m =1,2 n ≠ m. Characterizations concerning these concepts and several theorems are studied, where j = q , δ, a , pre, b, b.

In this paper, Nordhaus-Gaddum type relations on open support independence number of some derived graphs of path related graphs under addition and multiplication are studied.

Abstract. Fibrewise micro-topological spaces be a useful tool in various branches of mathematics. These mathematical objects are constructed by assigning a micro-topology to each fibre from a fibre bundle. The fibrewise micro-topological space is then formed by taking the direct limit of these individual micro-topological spaces. It can be adapted to analyze various mathematical structures, from algebraic geometry to differential equations. In this study, we delve into the generalizations of fibrewise micro-topological spaces and explore the applications of these abstract structures in different branches of mathematics. This study aims to define the fibrewise micro topological space through the generalizations that we use in this paper, whi

The ultimate goal of any sale contract is to maximize the combined returns of the parties, knowing that these returns are not realized (in long-term contracts) except in the final stages of the contract. Therefore, this requires the parties to the contract to leave some elements open, including the price, because the adoption of a fixed price and inflexible will not be appropriate to meet their desires when contracting, especially with ignorance of matters beyond their will and may affect the market conditions, and the possibility of modifying the fixed price through The elimination is very limited, especially when the parties to the contract are equally in terms of economic strength. Hence, in order to respond to market uncertainties, the

In this paper we define and study new concepts of fibrewise topological spaces over B namely, fibrewise Lindelöf and locally Lindelöf topological spaces, which are generalizations of will-known concepts: Lindelöf topological space (1) "A topological space X is called a Lindelöf space if for every open cover of X has a countable subcover" and locally Lindelöf topological space (1) "A topological space X is called a locally Lindelöf space if for every point x in X, there exist a nbd U of x such that the closure of U in X is Lindelöf space". Either the new concepts are: "A fibrewise topological space X over B is called a fibrewise Lindelöf if the projection function p : X→B is Lindelöf" and "The fibrewise topological space X over B

In this paper, some basic notions and facts in the b-modular space similar to those in the modular spaces as a type of generalization are given.  For example, concepts of convergence, best approximate, uniformly convexity etc. And then, two results about relation between semi compactness and approximation are proved which are used to prove a theorem on the existence of best approximation for a semi-compact subset of b-modular space.

This research is trying to study the Intellectual political structures of the Open Society according to British Thinker –with Austrian origin- Karl Popper (1902-1994). In First Axe we dealt with the context of Open and Closed society in the Popper's thought. While in the Second Axe we studied the Utopian and graduated Engineering. Finally in the third Axe  for the Rationalism, Freedom, Individualism, and the Democracy of Equality.