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top

Represents the universal top element or maximum value in mathematical logic and set theory.

Overview

Commonly used in lattice theory, order theory, and formal logic to denote the greatest element or universal upper bound of a partially ordered set.

  • Essential in abstract algebra for describing bounded lattices and complete lattices
  • Appears frequently in computer science when discussing type theory and formal semantics
  • Often paired with its dual symbol bottom (⊥) in mathematical proofs and formal specifications
  • Used in topology to represent the entire space or universal set

Examples

Using top symbol to denote the universal element in lattice theory

L={⊥,a,b,⊤}L = \{\bot, a, b, \top\} 
L = \{\bot, a, b, \top\}

Representing true value in logic notation

p∧⊤≡pp \land \top \equiv p 
p \land \top \equiv p

Denoting the entire space in topology

f−1(⊤)=Xf^{-1}(\top) = X 
f^{-1}(\top) = X