Every topological space Y admits a Γ-embedding into C(X,Y) for compact X, inducing partial actions on the function space from those on Y.
Dokuchaev,Partial actions: a survey, Groups, algebras and applications, XVIII Latin American algebra colloquium
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On {\Gamma}-embeddings and partial actions of function spaces
Every topological space Y admits a Γ-embedding into C(X,Y) for compact X, inducing partial actions on the function space from those on Y.