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...

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

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...

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

{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...

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

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

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

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

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

that subgraph isomorphism remains NP-complete even in the planar case. Subgraph isomorphism is a generalization of the graph isomorphism problem, which...

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

bijective correspondence. Thus, the definition of an isomorphism is quite natural. An isomorphism of groups may equivalently be defined as an invertible...

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...

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...

(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...

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

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

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...

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

of abstract algebra. He adopted this terminology because, using the isomorphism of the categories of Boolean algebras and of Boolean rings, the two notions...

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

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

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...

"there are two different groups of order 4 up to isomorphism", or "modulo isomorphism, there are two groups of order 4". This means that, if one considers...

this preorder is even a partial order (called the specialization order). On the other hand, for T1 spaces the order becomes trivial and is of little...

denoted NC ( S ) {\displaystyle {\text{NC}}(S)} . There is an obvious order isomorphism between NC ( S 1 ) {\displaystyle {\text{NC}}(S_{1})} and NC ( S 2...

homomorphism is an isomorphism if and only if it is bijective as a function on the underlying sets. If there exists a ring isomorphism between two rings...

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...