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15 relations: Comparison of topologies, Continuous function, Final topology, Helly metric, Inclusion map, Induced topology, Initial topology, List of mathematical jargon, Mathematics, Order topology, Quotient space (topology), Subset, Subspace topology, Topology, Total order.
Comparison of topologies
In topology and related areas of mathematics, the set of all possible topologies on a given set forms a partially ordered set.
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Continuous function
In mathematics, a continuous function is a function for which sufficiently small changes in the input result in arbitrarily small changes in the output.
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Final topology
In general topology and related areas of mathematics, the final topology (or strong, colimit, coinduced, or inductive topology) on a set X, with respect to a family of functions into X, is the finest topology on X which makes those functions continuous.
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Helly metric
In game theory, the Helly metric is used to assess the distance between two strategies.
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Inclusion map
In mathematics, if A is a subset of B, then the inclusion map (also inclusion function, insertion, or canonical injection) is the function \iota that sends each element, x, of A to x, treated as an element of B: A "hooked arrow" is sometimes used in place of the function arrow above to denote an inclusion map; thus: \iota: A\hookrightarrow B. (On the other hand, this notation is sometimes reserved for embeddings.) This and other analogous injective functions from substructures are sometimes called natural injections.
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Induced topology
In topology and related areas of mathematics, an induced topology on a topological space is a topology which makes the inducing function continuous from/to this topological space.
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Initial topology
In general topology and related areas of mathematics, the initial topology (or weak topology or limit topology or projective topology) on a set X, with respect to a family of functions on X, is the coarsest topology on X that makes those functions continuous.
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List of mathematical jargon
The language of mathematics has a vast vocabulary of specialist and technical terms.
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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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Order topology
In mathematics, an order topology is a certain topology that can be defined on any totally ordered set.
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Quotient space (topology)
In topology and related areas of mathematics, a quotient space (also called an identification space) is, intuitively speaking, the result of identifying or "gluing together" certain points of a given topological space.
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Subset
In mathematics, a set A is a subset of a set B, or equivalently B is a superset of A, if A is "contained" inside B, that is, all elements of A are also elements of B. A and B may coincide.
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Subspace topology
In topology and related areas of mathematics, a subspace of a topological space X is a subset S of X which is equipped with a topology induced from that of X called the subspace topology (or the relative topology, or the induced topology, or the trace topology).
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Topology
In mathematics, topology (from the Greek τόπος, place, and λόγος, study) is concerned with the properties of space that are preserved under continuous deformations, such as stretching, crumpling and bending, but not tearing or gluing.
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Total order
In mathematics, a linear order, total order, simple order, or (non-strict) ordering is a binary relation on some set X, which is antisymmetric, transitive, and a connex relation.
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