Definition:Upper Bound/Ordered Set

Definition

Let $\left({S, \preceq}\right)$ be a poset.

Let $T \subseteq S$ be bounded above in $S$ by an element $M \in S$.

Then $M$ is an upper bound for $T$.

Also see

• Lower Bound
• Bounded Below
• Bounded Above
• Bounded

Sources

• Paul R. Halmos: Naive Set Theory (1960)... (previous)... (next): $\S 14$: Order
• W.E. Deskins: Abstract Algebra (1964): Exercise $\S 2.3: 4$
• Steven A. Gaal: Point Set Topology (1964)... (previous)... (next): Introduction to Set Theory: $3$. The Axiom of Choice and Its Equivalents
• Seth Warner: Modern Algebra (1965)... (previous)... (next): $\S 14$
• T.S. Blyth: Set Theory and Abstract Algebra (1975): $\S 7$
• W.A. Sutherland: Introduction to Metric and Topological Spaces (1975): $\S 1.1$
• K.G. Binmore: Mathematical Analysis: A Straightforward Approach (1977)... (previous)... (next): $\S 2.2$
• Thomas A. Whitelaw: An Introduction to Abstract Algebra (1978)... (previous)... (next): $\S 10$