Meaning of superproperty | Babel Free

Definitions

1. A higher-level property in a hierarchy of properties.
2. A property of an infinite dimensional Banach space E such that for any infinite dimensional Banach space F, F↪E, has that same property.

Examples

“Just as a classes can be specialized with subclass relationships, properties can be specialized with subproperties. The “rdfs:subPropertyOf” property is used to specify a specialization relationship between properties. The described property is a subproperty of the indicated superproperty.”

“For our second principle we need the concept of superproperty. If (P) is a property of infinite dimensional Banach spaces, e.g. reflexivity, cotype, etc. we say that the infinite dimensional Banach space E has super (P) if any infinite dimensional Banach space F, F#92;hookrightarrowE, has property (P). If (P) = super (P), i.e. if a Banach space has super (P) if and only if it has (P) we call (P) a superproperty.”

CEFR level