## Abstract

The 1-covering property of omega limit sets is established for monotone and uniformly stable skew-product semiflows with the componentwise separating property of bounded and ordered full orbits. Then these results are applied to study the asymptotic almost periodicity of solutions to almost periodic reaction-diffusion equations and differential systems with time delays. The earlier convergence results for autonomous and periodic monotone systems are generalized to the almost periodic case without the strong monotonicity assumption.

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