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Zero-dimensional space

In mathematics, a zero-dimensional topological space (or nildimensional) is a topological space that has dimension zero with respect to one of several inequivalent notions of assigning a dimension to a given topological space. [1]

26 relations: Baire space (set theory), Base (topology), Cantor cube, Cantor space, Clopen set, Countable set, Cover (topology), Descriptive set theory, Dimension, Discrete space, Hausdorff space, Inductive dimension, Lebesgue covering dimension, Locally compact space, Mathematics, Metrization theorem, Open set, PlanetMath, Point (geometry), Polish space, Power set, Ryszard Engelking, Separable space, Subspace topology, Topological space, Totally disconnected space.

Baire space (set theory)

In set theory, the Baire space is the set of all infinite sequences of natural numbers with a certain topology.

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Base (topology)

In mathematics, a base (or basis) B for a topological space X with topology T is a collection of open sets in T such that every open set in T can be written as a union of elements of B.We are using a convention that the union of empty collection of sets is the empty set.

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Cantor cube

In mathematics, a Cantor cube is a topological group of the form A for some index set A. Its algebraic and topological structures are the group direct product and product topology over the cyclic group of order 2 (which is itself given the discrete topology).

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Cantor space

In mathematics, a Cantor space, named for Georg Cantor, is a topological abstraction of the classical Cantor set: a topological space is a Cantor space if it is homeomorphic to the Cantor set.

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Clopen set

In topology, a clopen set (a portmanteau of closed-open set) in a topological space is a set which is both open and closed.

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Countable set

In mathematics, a countable set is a set with the same cardinality (number of elements) as some subset of the set of natural numbers.

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Cover (topology)

In mathematics, a cover of a set X is a collection of sets whose union contains X as a subset.

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Descriptive set theory

In mathematical logic, descriptive set theory is the study of certain classes of "well-behaved" subsets of the real line and other Polish spaces.

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Dimension

In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it.

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Discrete space

In topology, a discrete space is a particularly simple example of a topological space or similar structure, one in which the points form a discontinuous sequence, meaning they are isolated from each other in a certain sense.

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Hausdorff space

In topology and related branches of mathematics, a Hausdorff space, separated space or T2 space is a topological space in which distinct points have disjoint neighbourhoods.

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Inductive dimension

In the mathematical field of topology, the inductive dimension of a topological space X is either of two values, the small inductive dimension ind(X) or the large inductive dimension Ind(X).

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Lebesgue covering dimension

In mathematics, the Lebesgue covering dimension or topological dimension of a topological space is one of several different ways of defining the dimension of the space in a topologically invariant way.

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Locally compact space

In topology and related branches of mathematics, a topological space is called locally compact if, roughly speaking, each small portion of the space looks like a small portion of a compact space.

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Mathematics

Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study of topics such as quantity (numbers), structure, space, and change.

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Metrization theorem

In topology and related areas of mathematics, a metrizable space is a topological space that is homeomorphic to a metric space.

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Open set

In topology, an open set is an abstract concept generalizing the idea of an open interval in the real line.

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PlanetMath

PlanetMath is a free, collaborative, online mathematics encyclopedia.

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Point (geometry)

In modern mathematics, a point refers usually to an element of some set called a space.

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Polish space

In the mathematical discipline of general topology, a Polish space is a separable completely metrizable topological space; that is, a space homeomorphic to a complete metric space that has a countable dense subset.

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Power set

In mathematics, the power set (or powerset) of any set, written, ℘(),, or 2''S'', is the set of all subsets of, including the empty set and itself.

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Ryszard Engelking

Ryszard Engelking (born 1935 in Sosnowiec) is a Polish mathematician.

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Separable space

In mathematics a topological space is called separable if it contains a countable, dense subset; that is, there exists a sequence \_^ of elements of the space such that every nonempty open subset of the space contains at least one element of the sequence.

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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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Topological space

In topology and related branches of mathematics, a topological space may be defined as a set of points, along with a set of neighbourhoods for each point, that satisfy a set of axioms relating points and neighbourhoods.

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Totally disconnected space

In topology and related branches of mathematics, a totally disconnected space is a topological space that is maximally disconnected, in the sense that it has no non-trivial connected subsets.

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Redirects here:

0-dimentional, 0-dimentional space, 0-polytope, Nildimensional space, Zero dimensional, Zero dimensional space, Zero-dimensional, Zeroth dimension.

References

[1] https://en.wikipedia.org/wiki/Zero-dimensional_space

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