We introduce the notion of an essential copy in a topological space. Then we present a classification of topological spaces based on this notion. In addition, we obtain some results regarding this classification.

In this article, we study the eigenvalues and potential functions of Sturm-Liouville operators with ordinary separated-type boundary condition. When the gap of the first two eigenvalues reaches minimum, we give the specific form of potential function. Meanwhile, for step potential function, we establish an one-to-one relationship between the eigenvalues and the nonnegative real roots of a class of algebraic equation, which provide an effective method for the approximate calculation of eigenvalues

In this paper, we prove a common fixed point theorem for occasionally weakly compatible mappings on fuzzy metric space satisfying an implicit relation. Our result never requires the completeness (or closedness) of the whole space (or subspaces), containment of ranges amongst involved mappings and continuity of one or more mappings. Our result improves and extends the results of Altun and Turkoglu [Commun. Korean Math. Soc.,23, 111-124 (2008)].

The existence and uniqueness of solution for the first order impulsive differential equation is established. We show that these results can be applied to second order impulsive differential equation. Examples are given to illustrate our main results

The main goal in this paper is to continue the investigations of the important system (see [4]), by considering a delayed multi-team prey- predator model. In the absence of delay, we study the conditions of the existence and stability properties of the equilibrium points. For the full general model with delay,conditions are derived under which there can be no change in stability. Using the discrete time delay as a bifurcation parameter it is found that Hopfbifurcation occurs when the delay passes through a critical value. Results are verified by computer simulation.