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Interpolation sets in spaces of continuous metric-valued functions
Let and be a topological space and metric space, respectively. If
denotes the set of all continuous functions from X to M, we say that a
subset of is an \emph{-interpolation set} if given any function
with relatively compact range in , there exists a map such that . In this paper, motivated by a result of Bourgain
in \cite{Bourgain1977}, we introduce a property, stronger than the mere
\emph{non equicontinuity} of a family of continuous functions, that isolates a
crucial fact for the existence of interpolation sets in fairly general
settings. As a consequence, we establish the existence of sets in every
nonprecompact subset of a abelian locally -groups. This implies
that abelian locally -groups strongly respects compactness
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