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searching for Complete metric space 28 found (110 total)

Polish space (1,479 words) [view diff] exact match in snippet view article find links to article

metrizable topological space; that is, a space homeomorphic to a complete metric space that has a countable dense subset. Polish spaces are so named because

Hadamard space (716 words) [view diff] exact match in snippet view article find links to article

complete CAT(0) spaces. A Hadamard space is defined to be a nonempty complete metric space such that, given any points x {\displaystyle x} and y , {\displaystyle

Kolmogorov continuity theorem (344 words) [view diff] exact match in snippet view article find links to article

Nikolaevich Kolmogorov. Let ( S , d ) {\displaystyle (S,d)} be some complete metric space, and let X : [ 0 , + ∞ ) × Ω → S {\displaystyle X\colon [0,+\infty

Banach–Mazur game (1,473 words) [view diff] exact match in snippet view article find links to article

countable union of nowhere-dense sets). If Y {\displaystyle Y} is a complete metric space, P 1 {\displaystyle P_{1}} has a winning strategy if and only if

Hopf–Rinow theorem (912 words) [view diff] exact match in snippet view article find links to article

subsets of M {\displaystyle M} are compact; M {\displaystyle M} is a complete metric space; M {\displaystyle M} is geodesically complete; that is, for every

Urysohn universal space (390 words) [view diff] exact match in snippet view article find links to article

"homogeneity" actually characterizes Urysohn universal spaces: A separable complete metric space that contains an isometric image of every separable metric space

Porous set (358 words) [view diff] exact match in snippet view article find links to article

meagre sets or measure zero sets, as shown below. Let (X, d) be a complete metric space and let E be a subset of X. Let B(x, r) denote the closed ball in

Hilbert cube (826 words) [view diff] exact match in snippet view article find links to article

Polish space, a topological space homeomorphic to a separable and complete metric space. Conversely, every Polish space is homeomorphic to a Gδ-subset of

Webbed space (1,340 words) [view diff] exact match in snippet view article find links to article

space – A locally convex topological vector space that is also a complete metric space Kakutani fixed-point theorem – Fixed-point theorem for set-valued

Fréchet mean (763 words) [view diff] exact match in snippet view article find links to article

Fréchet means for different distance functions. Let (M, d) be a complete metric space. Let x1, x2, …, xN be points in M. For any point p in M, define

Dense set (1,911 words) [view diff] exact match in snippet view article find links to article

{\displaystyle \left\{U_{n}\right\}} is a sequence of dense open sets in a complete metric space, X , {\displaystyle X,} then ⋂ n = 1 ∞ U n {\textstyle \bigcap _{n=1}^{\infty

Topological tensor product (1,845 words) [view diff] exact match in snippet view article find links to article

space – A locally convex topological vector space that is also a complete metric space Fredholm kernel – type of a kernel on a Banach spacePages displaying

Earle–Hamilton fixed-point theorem (830 words) [view diff] exact match in snippet view article find links to article

Earle-Hamilton theorem applies. The bounded symmetric domain D = G / K is a complete metric space for the Bergman metric. The open semigroup of the complexification

Ideal theory (1,095 words) [view diff] exact match in snippet view article find links to article

Z {\displaystyle \mathbb {Z} } can be completed. The resulting complete metric space has a structure of a ring that extended the ring structure of Z

Rational number (3,494 words) [view diff] exact match in snippet view article find links to article

is also totally disconnected. The rational numbers do not form a complete metric space, and the real numbers are the completion of Q {\displaystyle \mathbb

Delta-convergence (542 words) [view diff] exact match in snippet view article find links to article

states that if ( X , d ) {\displaystyle (X,d)} is an asymptotically complete metric space, then every bounded sequence in X {\displaystyle X} has a Delta-convergent

Complete Boolean algebra (1,347 words) [view diff] exact match in snippet view article find links to article

metric space and B its completion then any isometry from A to a complete metric space C can be extended to a unique isometry from B to C. The analogous

Radon measure (2,697 words) [view diff] exact match in snippet view article find links to article

(positive) Radon measures on X can be given the structure of a complete metric space by defining the Radon distance between two measures m1, m2 ∈ M+(X)

Irrational number (5,253 words) [view diff] exact match in snippet view article find links to article

G-delta set—i.e., a countable intersection of open subsets—in a complete metric space, the space of irrationals is completely metrizable: that is, there

Hausdorff dimension (3,147 words) [view diff] exact match in snippet view article find links to article

Banach's contractive mapping fixed point theorem applied to the complete metric space of non-empty compact subsets of Rn with the Hausdorff distance.

Hardy space (4,345 words) [view diff] exact match in snippet view article find links to article

Hardy space Hp, which defines the topology and makes Hp into a complete metric space. When 0 < p ≤ 1, a bounded measurable function f of compact support

General topology (5,724 words) [view diff] exact match in snippet view article find links to article

come from a metric. The Baire category theorem says: If X is a complete metric space or a locally compact Hausdorff space, then the interior of every

Uniform continuity (4,148 words) [view diff] exact match in snippet view article find links to article

{\displaystyle S} a subset of X {\displaystyle X} , R {\displaystyle R} a complete metric space, and f : S → R {\displaystyle f:S\rightarrow R} a continuous function

Σ-algebra (5,337 words) [view diff] exact match in snippet view article find links to article

_{S}\right)} is a standard Borel space (for example, a separable complete metric space with its associated Borel sets), then the converse is also true

Glossary of topology (7,583 words) [view diff] exact match in snippet view article find links to article

completely metrizable, i.e. if it is homeomorphic to a separable and complete metric space. Polyadic A space is polyadic if it is the continuous image of the

Formal power series (9,656 words) [view diff] exact match in snippet view article find links to article

{\displaystyle R[[X]]} the structure of a topological ring (and even of a complete metric space). But the general construction of a completion of a metric space

Fréchet algebra (3,459 words) [view diff] exact match in snippet view article find links to article

the requirement for the algebra to be locally convex, but still a complete metric space. In this case, the underlying space may be called a Fréchet space

Glossary of set theory (11,511 words) [view diff] exact match in snippet view article find links to article

Polish space is a separable topological space homeomorphic to a complete metric space pow Abbreviation for "power (set)" power "Power" is an archaic term