= Cb-embedded subset
{c}
{title2=$C^b(Y)=C^b(X)|_Y$}
A <subset> is <Cb-embedded subset>[Cb-embedded] if every bounded <continuous> <real-valued function> on it extends to a bounded <continuous> <real-valued function> on the ambient space. A bounded extension can be clipped to preserve the original bound. This is weaker than <C-embedded subset>[C-embeddedness]: the <natural numbers> in their <Stone-Čech compactification> have the bounded extension property, but their unbounded identity <function> cannot extend to a <compact space>.
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