Compendium of Predicates
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  • 🌐Orientation
    • ⭐Welcome
    • ✒️Notation
    • 😅An Example
  • 🧰Definitions
    • Relation Taxonomy
    • Order Taxonomy
    • Algebra
      • Magma
      • Semigroup
      • Monoid
      • Group
      • Ringoid
      • Semiring
      • Ring
      • Unit Ring
      • Boolean Ring
      • Boolean Group
    • Bandler and Kohout Products of Relations
    • Closed
    • Complement
    • De Baets and Kerre Products of Relations
    • Extremal Elements
    • Galois Connection
    • Images of a set under a relation
    • Indexed Union and Intersection
    • Monoidal Preorder
    • Monotone Map
    • Natural Projection
    • Non-Preservation of Extrema
    • Over and Under
    • Power Set
    • Preorder
    • Preservation of Extrema
    • Product
    • Relation Inclusion
    • Row Constant Relations
    • Semilattice
    • Set Inclusion
    • Symmetric Monoidal Preorder
    • Upper Set
  • 🔬Checks
    • 🎙️A few words about the checks
    • Indirect Equality and Inclusion
    • Below
    • Extremal Elements
    • Relation Division
    • Algebra
      • Ring
      • Boolean Ring
      • Boolean Group
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  1. 🧰Definitions

Closed

Closed sets are elegantly described using coreflexives and inclusion

Closed  A  R  X\textbf{Closed} \; A \; R \; XClosedARX

EndoRelation  A  R\textbf{EndoRelation} \; A \; REndoRelationAR

PowerSet  A  X\textbf{PowerSet} \; A \; XPowerSetAX

ΦX;R⊆R;ΦX\Phi_X ; R \subseteq R ; \Phi_XΦX​;R⊆R;ΦX​


pred Closed(A: set univ, R: univ->univ, X: set univ) {
  EndoRelation[A,R]
  X in A
  X<:R in R:>X
}
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Last updated 1 year ago