noun, plural universalities.
the character or state of being universal; existence or prevalence everywhere.
relation, extension, or applicability to all.
universal character or range of knowledge, interests, etc.

1325–75; Middle English universalite < Late Latin ūniversālitās. See universal, -ity

nonuniversality, noun
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World English Dictionary
universality (ˌjuːnɪvɜːˈsælɪtɪ)
the state or quality of being universal

Collins English Dictionary - Complete & Unabridged 10th Edition
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Example sentences
And the idea of universality from simple principles, that you don't need much
  to get everything.
As the network spreads, it is fostering both the universality and the
  individuality of human discourse.
The sun and its planets share the universality of the building blocks of our
  quantum world: electrons, nucleons and photons.
In computer science lingo, that's called universality.
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