mathematical field of order theory, an order isomorphism is a special kind of monotone function that constitutes a suitable notion of isomorphism for partially...

isomorphic, with a unique isomorphism. The isomorphism theorems provide canonical isomorphisms that are not unique. The term isomorphism is mainly used for algebraic...

{P} (\mathbb {N} )} that is order-preserving, order-reflecting, and hence an order-embedding. It is not an order-isomorphism (since it, for instance, does...

the resulting isomorphism from Z n {\displaystyle \mathbb {Z} ^{n}} to the image of φ {\displaystyle \varphi } is an order isomorphism when the image...

An order isomorphism can be characterized as a surjective order embedding. As a consequence, any order embedding f restricts to an isomorphism between...

In order theory and model theory, branches of mathematics, Cantor's isomorphism theorem states that every two countable dense unbounded linear orders are...

the unique (up to an order isomorphism) "initial example" of a totally ordered set with a certain property, (here, a total order A is initial for a property...

same up to renaming of elements. Order isomorphisms are functions that define such a renaming. An order-isomorphism is a monotone bijective function that...

an order isomorphism is a surjective order embedding. Order-preserving. See monotone. Order-reversing. See antitone. Partial order. A partial order is...

where ω is the smallest limit ordinal. For example, there exists an order-isomorphism between the rational numbers and other densely ordered countable sets...

Look up isomorphism or isomorph in Wiktionary, the free dictionary. Isomorphism or isomorph may refer to: Isomorphism, in mathematics, logic, philosophy...

ordering. That is, f(a) ≤' f(b) if and only if a ≤ b. Provided there exists an order isomorphism between two well-ordered sets, the order isomorphism...

Monotonic Pointwise order of functions Galois connection Order embedding Order isomorphism Closure operator Functions that preserve suprema/infima Dedekind completion...

(y ∧ z) = (x ∨ y) ∧ (x ∨ z) holds Being a Boolean algebra Being an order isomorphism. Since partial orders are antisymmetric, the only ones that are self-dual...

rather weak compared to an order isomorphism between the involved posets, but every Galois connection gives rise to an isomorphism of certain sub-posets,...

well-ordered set, in a sense different from cardinality: if there is an order isomorphism (more than a bijection) between two well-ordered sets, they have the...

standard definition of isomorphisms as invertible morphisms, a lattice isomorphism is just a bijective lattice homomorphism. Similarly, a lattice endomorphism...

set" for well-ordered sets: ordinal number (equal if there is an order-isomorphism) Resizing (fiction), a theme in fiction, in particular in fairy tales...

First-order logic, also called predicate logic, predicate calculus, or quantificational logic, is a collection of formal systems used in mathematics,...

science: Can the graph isomorphism problem be solved in polynomial time? (more unsolved problems in computer science) The graph isomorphism problem is the computational...

In mathematics, a well-order (or well-ordering or well-order relation) on a set S is a total ordering on S with the property that every non-empty subset...

set" for well-ordered sets: ordinal number (equal if there is an order-isomorphism) In statistics (hypothesis testing), the "size" of the test refers...

specifically, in differential geometry—the musical isomorphism (or canonical isomorphism) is an isomorphism between the tangent bundle T M {\displaystyle \mathrm...

( x ) ≤ f ( y ) ) {\displaystyle f(x)\leq f(y))} and order isomorphisms (surjective order embeddings). In the context of search algorithms monotonicity...

partial order is—up to an order isomorphism—the Cartesian product of k = | S | {\displaystyle k=|S|} (the cardinality of S) copies of the partial order on...

with partial orders. Any bijective history preserving function is an order isomorphism. Furthermore, if for a given prefix ordered set P we construct the...

structure and the mapping x ↦ − x {\displaystyle x\mapsto -x} is an isomorphism to the dual order structure. Ordered vector spaces are ordered groups under their...

is called orderable or linearly orderable if there exists a total order on its elements such that the order topology induced by that order and the given...

{\displaystyle G^{-1}(x)<G^{-1}(y).} Therefore, G {\displaystyle G} is an order isomorphism from ( D o m ( G ) , < ) {\displaystyle (Dom(G),<)} to ( V , < ) ...

programs and mathematical proofs. It is also known as the Curry–Howard isomorphism or equivalence, or the proofs-as-programs and propositions- or formulae-as-types...