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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. 

## Baire space (set theory)

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

## 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.

## 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).

## 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.

## 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.

## 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.

## Cover (topology)

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

## Descriptive set theory

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

## 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.

## 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.

## 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.

## 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).

## 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.

## 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.

## Mathematics

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

## Metrization theorem

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

## Open set

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

## PlanetMath

PlanetMath is a free, collaborative, online mathematics encyclopedia.

## Point (geometry)

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

## 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.

## Power set

In mathematics, the power set (or powerset) of any set is the set of all subsets of, including the empty set and itself, variously denoted as, 𝒫(), ℘() (using the "Weierstrass p"),,, or, identifying the powerset of with the set of all functions from to a given set of two elements,.

## Ryszard Engelking

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

## 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.

## 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).

## 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, satisfying a set of axioms relating points and neighbourhoods.

## 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.

## References

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