# Category:Order Embeddings

This category contains results about Order Embeddings.

Definitions specific to this category can be found in Definitions/Order Embeddings.

Let $\left({S, \preceq_1}\right)$ and $\left({T, \preceq_2}\right)$ be ordered sets.

An **order embedding** is a mapping $\phi: S \to T$ such that:

- $\forall x, y \in S: x \preceq_1 y \iff \phi \left({x}\right) \preceq_2 \phi \left({y}\right)$

## Pages in category "Order Embeddings"

The following 15 pages are in this category, out of 15 total.

### E

### M

- Mapping from Totally Ordered Set is Dual Order Embedding iff Strictly Decreasing
- Mapping from Totally Ordered Set is Order Embedding iff Strictly Increasing
- Mapping from Totally Ordered Set is Order Embedding iff Strictly Increasing/Reverse Implication
- Mapping from Totally Ordered Set is Order Embedding iff Strictly Increasing/Reverse Implication/Proof 1
- Mapping from Totally Ordered Set is Order Embedding iff Strictly Increasing/Reverse Implication/Proof 2