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26 relations: Additive inverse, Automorphism, Bijection, Equivalence class, Equivalence relation, Function composition, Galois connection, Group isomorphism, Identity function, Interval (mathematics), Inverse function, Isomorphism, Mathematics, Monotonic function, Order embedding, Order theory, Order type, Partially ordered group, Partially ordered set, Permutation pattern, Real number, Reflexive relation, Surjective function, Symmetric relation, Transitive relation, Undergraduate Texts in Mathematics.
Additive inverse
In mathematics, the additive inverse of a number is the number that, when added to, yields zero.
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Automorphism
In mathematics, an automorphism is an isomorphism from a mathematical object to itself.
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Bijection
In mathematics, a bijection, bijective function, or one-to-one correspondence is a function between the elements of two sets, where each element of one set is paired with exactly one element of the other set, and each element of the other set is paired with exactly one element of the first set.
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Equivalence class
In mathematics, when the elements of some set S have a notion of equivalence (formalized as an equivalence relation) defined on them, then one may naturally split the set S into equivalence classes.
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Equivalence relation
In mathematics, an equivalence relation is a binary relation that is reflexive, symmetric and transitive.
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Function composition
In mathematics, function composition is the pointwise application of one function to the result of another to produce a third function.
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Galois connection
In mathematics, especially in order theory, a Galois connection is a particular correspondence (typically) between two partially ordered sets (posets).
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Group isomorphism
In abstract algebra, a group isomorphism is a function between two groups that sets up a one-to-one correspondence between the elements of the groups in a way that respects the given group operations.
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Identity function
Graph of the identity function on the real numbers In mathematics, an identity function, also called an identity relation or identity map or identity transformation, is a function that always returns the same value that was used as its argument.
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Interval (mathematics)
In mathematics, a (real) interval is a set of real numbers with the property that any number that lies between two numbers in the set is also included in the set.
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Inverse function
In mathematics, an inverse function (or anti-function) is a function that "reverses" another function: if the function applied to an input gives a result of, then applying its inverse function to gives the result, and vice versa.
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Isomorphism
In mathematics, an isomorphism (from the Ancient Greek: ἴσος isos "equal", and μορφή morphe "form" or "shape") is a homomorphism or morphism (i.e. a mathematical mapping) that can be reversed by an inverse morphism.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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Monotonic function
In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order.
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Order embedding
In mathematical order theory, an order embedding is a special kind of monotone function, which provides a way to include one partially ordered set into another.
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Order theory
Order theory is a branch of mathematics which investigates the intuitive notion of order using binary relations.
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Order type
In mathematics, especially in set theory, two ordered sets X,Y are said to have the same order type just when they are order isomorphic, that is, when there exists a bijection (each element matches exactly one in the other set) f: X → Y such that both f and its inverse are strictly increasing (order preserving i.e. the matching elements are also in the correct order).
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Partially ordered group
In abstract algebra, a partially ordered group is a group (G,+) equipped with a partial order "≤" that is translation-invariant; in other words, "≤" has the property that, for all a, b, and g in G, if a ≤ b then a+g ≤ b+g and g+a ≤ g+b.
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Partially ordered set
In mathematics, especially order theory, a partially ordered set (also poset) formalizes and generalizes the intuitive concept of an ordering, sequencing, or arrangement of the elements of a set.
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Permutation pattern
In combinatorial mathematics and theoretical computer science, a permutation pattern is a sub-permutation of a longer permutation.
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Real number
In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.
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Reflexive relation
In mathematics, a binary relation R over a set X is reflexive if every element of X is related to itself.
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Surjective function
In mathematics, a function f from a set X to a set Y is surjective (or onto), or a surjection, if for every element y in the codomain Y of f there is at least one element x in the domain X of f such that f(x).
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Symmetric relation
In mathematics and other areas, a binary relation R over a set X is symmetric if it holds for all a and b in X that a is related to b if and only if b is related to a. In mathematical notation, this is: Symmetry, along with reflexivity and transitivity, are the three defining properties of an equivalence relation.
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Transitive relation
In mathematics, a binary relation over a set is transitive if whenever an element is related to an element and is related to an element then is also related to.
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Undergraduate Texts in Mathematics
Undergraduate Texts in Mathematics (UTM) is a series of undergraduate-level textbooks in mathematics published by Springer-Verlag.
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Order automorphism, Order isomorphic, Order-automorphism, Order-isomorphic, Order-isomorphism.
References
[1] https://en.wikipedia.org/wiki/Order_isomorphism
