Construction of almost periodic functions with given properties

We define almost periodic functions with values in a pseudometric space X. We mention the Bohr and the Bochner definition of almost periodicity. We present one modifiable method for constructing almost periodic functions in X. Applying this method, we prove that in any neighbourhood of an almost periodic skew-Hermitian linear differential system there exists a system which does not possess a nontrivial almost periodic solution.

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