Abstract
In order to determine the dynamics of nonautonomous equations both their forward and pullback behavior need to be understood. For this reason we provide sufficient criteria for the existence of such attracting invariant sets in a general setting of nonautonomous difference equations in metric spaces. In addition it is shown that both forward and pullback attractors, as well as forward limit sets persist and that the latter two notions even converge under perturbation.As concrete application, we study integrodifference equations over the continuous functions under spatial discretization of collocation type. Integrodifference equation and Pullback attractor and Forward attractor and Urysohn operator
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