(M, d) is a bounded metric space (or d is a bounded metric) if M is bounded as a subset of itself. Total boundedness implies boundedness. For subsets...

is bounded. (However, a continuous function must be bounded if its domain is both closed and bounded.) Bounded set Compact support Local boundedness Uniform...

mathematics, total-boundedness is a generalization of compactness for circumstances in which a set is not necessarily closed. A totally bounded set can be covered...

analysis and related areas of mathematics, a set in a topological vector space is called bounded or von Neumann bounded, if every neighborhood of the zero vector...

bounded if it is bounded around every point. A family of functions is locally bounded if for any point in their domain all the functions are bounded around...

is bounded. Function bounded on a neighborhood and local boundedness In contrast, a map F : X → Y {\displaystyle F:X\to Y} is said to be bounded on a...

lower) bound is said to be bounded from above or majorized (respectively bounded from below or minorized) by that bound. The terms bounded above (bounded below)...

{\displaystyle Y} is Banach. Bounded set (topological vector space) – Generalization of boundedness Contraction (operator theory) – Bounded operators with sub-unit...

In mathematics, particularly in mathematical logic and set theory, a club set is a subset of a limit ordinal that is closed under the order topology, and...

Precompact set may refer to: Relatively compact subspace, a subset whose closure is compact Totally bounded set, a subset that can be covered by finitely...

( 0 ) ) {\displaystyle f_{c}(f_{c}(0))} , etc., remains bounded in absolute value. This set was first defined and drawn by Robert W. Brooks and Peter...

lesion or in geology concerning a rock. A bounded set is a set whose diameter is finite. Within a bounded set, all distances are at most the diameter....

{\displaystyle X} that map every order interval into a bounded set is called the order bound dual of X {\displaystyle X} and denoted by X b . {\displaystyle...

and the other is to study notions related to boundedness (vector bornologies, bounded operators, bounded subsets, etc.). For normed spaces, from which...

locally bounded (i.e. maps bounded sets to bounded sets). A linear map between two TVSs is called infrabounded if it maps Banach disks to bounded disks...

bounded open set is not necessarily Jordan measurable. For example, the complement of the fat Cantor set (within the interval) is not. A bounded set is...

Look up bounded in Wiktionary, the free dictionary. Boundedness, bounded, or unbounded may refer to: Bounded rationality, the idea that human rationality...

definition of boundedness can be weakened a bit; E {\displaystyle E} is bounded if and only if every countable subset of it is bounded. A set is bounded if and...

closed and bounded sets in Rn The Weierstrass extreme value theorem, which states that a continuous function on a closed and bounded set obtains its...

Heine–Borel property (R.E. Edwards uses the term boundedly compact space) if each closed bounded set in X {\displaystyle X} is compact. No infinite-dimensional...

"∃". Bounded quantifiers differ from "∀" and "∃" in that bounded quantifiers restrict the range of the quantified variable. The study of bounded quantifiers...

is complete if and only if every bounded set that is closed in the order topology is compact. A totally ordered set (with its order topology) which is...

polytopes to be unbounded. The terms "bounded/unbounded convex polytope" will be used below whenever the boundedness is critical to the discussed issue....

to take convex combinations of points. Absorbing set Algorithmic problems on convex sets Bounded set (topological vector space) Brouwer fixed-point theorem...

set. In this case the problem has no solution and is said to be infeasible. Feasible sets may be bounded or unbounded. For example, the feasible set defined...

mathematics, a function of bounded mean oscillation, also known as a BMO function, is a real-valued function whose mean oscillation is bounded (finite). The space...

approach to increase their utility. In addition to bounded rationality, bounded willpower and bounded selfishness are two other key concepts in behavioral...

be non-empty and bounded (finite). Bounding volumes are most often used to accelerate certain kinds of tests. In ray tracing, bounding volumes are used...

Balanced set – Construct in functional analysis Bounded set (topological vector space) – Generalization of boundedness Convex set – In geometry, set whose...

there exists a countable set B {\displaystyle {\mathcal {B}}} of bounded subsets of X {\displaystyle X} such that every bounded subset of X {\displaystyle...