We define and study new ideas of fibrewise topological space namely fibrewise multi-topological space . We also submit the relevance of fibrewise closed and open topological space . Also fibrewise multi-locally sliceable and fibrewise multi-locally section able multi-topological space . Furthermore, we propose and prove a number of statements about these ideas. On the other hand, extend separation axioms of ordinary topology into fibrewise setting. The separation axioms are said to be fibrewise multi-T0. spaces, fibrewise multi-T1spaces, fibrewise multi-R0 spaces, fibrewise multi-Hausdorff spaces, fibrewise multi-functionally Hausdorff spaces, fibrewise multi-regular spaces, fibrewise multi-completely regular spaces, fibrewise multi-normal

     In this paper we introduce a new class of sets called -generalized b- closed (briefly gb closed) sets. We study some of its basic properties. This class of sets is strictly placed between the class of gp- closed sets and the class of gsp- closed sets. Further the notion of b- space is introduced and studied.

2000 Mathematics Subject Classification: 54A05

Our goal in this work is to describe the structure of a class of bimodal self maps on the compact real interval I with zero topological entropy and transitive.

In this paper, a new idea to configure a special graph from the discrete topological space is given. Several properties and bounds of this topological graph are introduced. Such that if the order of the non-empty set equals two, then the topological graph is isomorphic to the complete graph. If the order equals three, then the topological graph is isomorphic to the complement of the cycle graph. Our topological graph has  complete induced subgraphs with order  or more. It also has a cycle subgraph. In addition, the clique number is obtained. The topological graph is proved simple, undirected, connected graph. It has no pendant vertex, no isolated vertex and no cut vertex. The minimum and maximum degrees are evaluated. So , the radius 

       This paper treats the interactions among four population species. The system includes one mutuality prey, one harvested prey and two predators. The four species interaction can be described as a food chain, where the first prey helps the second harvested prey. The first and the second predator attack the first and the second prey, respectively, according to Lotka-Volterra type functional responses. The model is formulated using differential equations. One equilibrium point of the model is found and analysed to reveal a threshold that will allow the coexistence of all species. All other equilibrium points of the system are located, with their local and global stability being assessed. To back up the conclusions of the mathema

In this paper, a mathematical model was built for the supply chain to reduce production, inventory, and transportation in Baghdad Company for Soft Drink. The linear programming method was used to solve this mathematical model. We reduced the cost of production by reduced the daily work hours, the company do not need the overtime hours to work at the same levels of production, and the costs of storage in the company's warehouses and agents' stores have been reduced by making use of the stock correctly, which guarantees reducing costs and preserving products from damage. The units transferred from the company were equal to the units demanded by the agents. The company's mathematical model also achieved profits by (84,663,769) by re

The goal of the research is to introduce new types of maps called semi totally Bc-continuous map and totally Bc-continuous map furthermore, study its properties. Additionally, we study the relationship of these functions and other known mappings are discussed.

     In this paper, the aquatic food chain model, consisting of Phytoplankton, Zooplankton, and Fish, in the contaminated environment is proposed and studied. Modified Leslie–Gower model with Holling type IV functional response are used to describe the growth of Fish and the food transition throughout the food chain, respectively. The toxic substance affects directly the Phytoplankton and indirectly the other species. The local stability analysis of all possible equilibrium points is done. The persistence conditions of the model are established. The basin of attraction for each point is specified using the Lyapunov function. Bifurcation analysis near the coexistence equilibrium point is investigated. Detecting the existence of chao

In this work, we consider a modification of the Lotka-Volterra food chain model of three species, each of them is growing logistically. We found that the model has eight equilibrium points, four of them always exist, while the rest exist under certain conditions. In terms of stability, we found that the system has five unstable equilibrium points, while the rest points are locally asymptotically stable under certain satisfying conditions. Finally, we provide an example to support the theoretical results.