Relation sumo#closed_on (pm#function_type,sumo#set_or_class)  a binary_function is closed on a set_or_class if it is defined for all instances of the set_or_class and its value is always an instance of the set_or_class
  type:  pm#binary_predicate_type  the class of predicates relating two items - its valence is two
  type:  pm#asymmetric_relation_type  an antisymmetric and irreflexive relation
  supertype:  pm#relation_to_set_or_class (*,pm#set_or_class)
     supertype:  pm#relation_to_collection (*,pm#collection)
        supertype:  pm#relation_from/to_thing_of_common_kind (*)  this type permits to categorize relations according to their signatures and hence offers (i) a concise way to set essential exclusion relations, and (ii) a systematic and easy-to-follow categorization
           >part of:  pm#relation__related_thing__relatedthing___related_with  type for any relation (unary, binary, ..., *-ary) and instance of pm#relation_type
        supertype:  pm#what_relation (*)
           supertype:  pm#wh-/how_relation (*)  this type permits to categorize relations according to the usual who/what/why/where/when/how questions ; this is a traditional but very subjective and ineffective way of categorizing relations 
              >part of:  pm#relation__related_thing__relatedthing___related_with  type for any relation (unary, binary, ..., *-ary) and instance of pm#relation_type
  supertype:  pm#asymmetric_relation (?,?)  this category only serves structuration purposes: it is instance of pm#asymmetric_relation_type which is not instance of pm#class_of_inheritable_relation_type
     supertype:  pm#irreflexive_relation__irreflexiverelation (?,?)  this category only serves structuration purposes: it is instance of pm#irreflexive_relation_type which is not instance of pm#class_of_inheritable_relation_type
        supertype:  pm#binary_relation_with_particular_mathematical_property (?,?)
           supertype:  pm#relation_with_particular_mathematical_property (*)
              supertype:  pm#relation_with_particular_property (*)  this rather fuzzy type permits to group categorization schemes less common than those covered by the previous sibling categories
                 >part of:  pm#relation__related_thing__relatedthing___related_with  type for any relation (unary, binary, ..., *-ary) and instance of pm#relation_type
     supertype:  pm#antisymmetric_relation__antisymmetricrelation (?,?)  this category only serves structuration purposes: it is instance of pm#antisymmetric_relation_type which is not instance of pm#class_of_inheritable_relation_type
        supertype:  pm#binary_relation_with_particular_mathematical_property (?,?)