Order, lattices, ordered algebraic structures Maps between ordered sets Concept
Monotone function
Summary
A monotone function between ordered sets is a function that keeps the order.
Where this leads
22 pages build on this one.
- Dedekind number
- XYZ inequality
- Stieltjes function
- Nerve of a category
- Order polytope
- FKG inequality
- Simplicial set
- Lattice homomorphism
- Simplex category
- Davis's converse of the Knaster–Tarski theorem
- Operator monotone function
- Fixed-point property of posets
- Knaster–Tarski theorem
- Monotone cubic interpolation
- Abian–Brown theorem
- Scott continuity
- Simplicial object
- Harris inequality
- Post's functional completeness theorem
- Order polynomial
- Lebesgue–Stieltjes measure
- Cauchy's functional equation
Further reading
- Web https://en.wikipedia.org/wiki/Monotonic_function, In order theory
About this page
| Tag | 0A7KV2WB7A |
|---|---|
| URI | m2://0A7KV2WB7A |
| Aliases | order-preserving-function, monotonic-function, isotone |
| Kind | concept |
| Writing | W1 stated |
| MSC | 06A06 |
| Same as |
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What this page needs for W2
- edge instance_of in: at least two examples (0 of 2)
- edge not_instance_of in: at least one non-example (0 of 1)
The writing levels say how complete the text of a page is. They do not measure its truth.
What links here
Special cases
- Strictly monotone function
- Order isomorphism
- Operator monotone function
- Order embedding
- Stieltjes function
Definitions
Results about this
Used by
- Dedekind number
- Stieltjes function
- Order polytope
- FKG inequality
- Lattice homomorphism
- Simplex category
- Davis's converse of the Knaster–Tarski theorem
- Operator monotone function
- Fixed-point property of posets
- Knaster–Tarski theorem
- Monotone cubic interpolation
- Abian–Brown theorem
- Scott continuity
- Harris inequality
- Post's functional completeness theorem
- Order polynomial
- Lebesgue–Stieltjes measure
- Cauchy's functional equation