spaces can be embedded in the Hilbert cube; that is, can be viewed as subspaces of the Hilbert cube (see below). The Hilbert cube is best defined as the topological...

theorem implies that every Hilbert cube manifold as well as the (rather different, for example not locally compact) Hilbert manifolds and Banach manifolds...

geometry, a hypercube is an n-dimensional analogue of a square (n = 2) and a cube (n = 3); the special case for n = 4 is known as a tesseract. It is a closed...

countable open set. Every Polish space is homeomorphic to a Gδ-subset of the Hilbert cube (that is, of IN, where I is the unit interval and N is the set of natural...

tesseract. A tesseract is a cube analogous' four-dimensional space bounded by twenty-four squares and eight cubes. Hilbert's third problem asked whether...

David Hilbert Foundations of geometry Hilbert C*-module Hilbert cube Hilbert curve Hilbert matrix Hilbert metric Hilbert–Mumford criterion Hilbert number...

space is homeomorphic to a Gδ subspace of the Hilbert cube, and every Gδ subspace of the Hilbert cube is Polish. Every Polish space is obtained as a...

the Hilbert cube as an example of a compact space; there is no contradiction because the cube cannot be a neighbourhood of any point in Hilbert space...

exist in specific contexts. These include non-separable spaces like the Hilbert cube, or scenarios where some typical properties of finite-dimensional Lebesgue...

Extended real number line Finite topological space Hawaiian earring Hilbert cube Irrational cable on a torus Lakes of Wada Long line Order topology...

characterized as those spaces which are homeomorphic to a subspace of the Hilbert cube [ 0 , 1 ] N , {\displaystyle \lbrack 0,1\rbrack ^{\mathbb {N} },} that...

the continuum hypothesis is true The following example is based on the Hilbert cube. Let Rω denote the countable cartesian product of R with itself, i.e...

commutative unital Banach algebra is a compact Hausdorff space. The Hilbert cube is compact, again a consequence of Tychonoff's theorem. A profinite group...

metrizable. Every separable metric space is homeomorphic to a subset of the Hilbert cube. This is established in the proof of the Urysohn metrization theorem...

{\displaystyle I_{s}=I} . The Hilbert cube, I ℵ 0 {\displaystyle I^{\aleph _{0}}} , is a special case of a Tychonoff cube. The axiom of choice is assumed...

selections in all pairs of axes are rhombi. Minimum bounding rectangle Cuboid Hilbert cube N.W. Johnson: Geometries and Transformations, (2018) ISBN 978-1-107-10340-5...

that is not contractible, and therefore different from an n-cell. The Hilbert cube is an infinite-dimensional continuum. Solenoids are among the simplest...

Einstein–Hilbert equations Hilbert algebra Hilbert C*-module Hilbert basis (linear programming) Hilbert class field Hilbert cube Hilbert curve Hilbert curve...

Cantor cube Space-filling curve Topologist's sine curve Tychonoff plank Comb space Uniform norm Weak topology Strong topology Hilbert cube Lower limit...

compact, contractible, path connected and locally path connected. The Hilbert cube is obtained by taking a topological product of countably many copies...

and algebra, the cube of a number n is its third power, that is, the result of multiplying three instances of n together. The cube of a number n is denoted...

nonempty compact connected metric space. The arc, the n-sphere, and the Hilbert cube are examples of path-connected continua; the topologist's sine curve...

compactification topology One point compactification of the rationals Hilbert space Fréchet space Hilbert cube Order topology Open ordinal space [0,Γ) where Γ<Ω Closed...

homeomorphic to a Hilbert cube. Compact space – Type of mathematical space General linear group – Group of n × n invertible matrices Cube "The Banach–Mazur...

cubes problem, discusses whether every integer is the sum of four cubes of integers Hilbert, David (1909). "Beweis für die Darstellbarkeit der ganzen Zahlen...

of the exclusion of a particular point. Fort space Half-disk topology Hilbert cube − [ 0 , 1 / 1 ] × [ 0 , 1 / 2 ] × [ 0 , 1 / 3 ] × ⋯ {\displaystyle [0...

topology. Much of his early work focused on proofs surrounding Hilbert space and Hilbert cubes. Richard Anderson and his twin brother, John, were born February...

Fujita, Masahisa (2008). "Knowledge Creation As A Square Dance On The Hilbert Cube". International Economic Review. 49 (4): 1251–1295. CiteSeerX 10.1.1...

Infinite-dimensional topology See Hilbert manifold and Q-manifolds, i.e. (generalized) manifolds modelled on the Hilbert space and on the Hilbert cube respectively. Inner...

groups P n {\displaystyle P_{n}} and to the fundamental group of the Hilbert cube minus the set { ( x i ) i ∈ N ∣ x i = x j  for some  i ≠ j } . {\displaystyle...