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The word "bounded" makes no sense in a general topological space without a corresponding metric. Boundary is a distinct concept; for example, a circle (not to be confused with a disk) in isolation is a boundaryless bounded set, while the half plane is unbounded yet has a boundary. A bounded set is not necessarily a closed set and vice
The collection of all bounded sets on a topological vector space is called the von Neumann bornology or the (canonical) bornology of .. A base or fundamental system of bounded sets of is a set of bounded subsets of such that every bounded subset of is a subset of some . [1] The set of all bounded subsets of trivially forms a fundamental system of bounded sets of .
OCaml's standard library contains a Set module, which implements a functional set data structure using binary search trees. The GHC implementation of Haskell provides a Data.Set module, which implements immutable sets using binary search trees. [9] The Tcl Tcllib package provides a set module which implements a set data structure based upon TCL ...
A data structure known as a hash table.. In computer science, a data structure is a data organization and storage format that is usually chosen for efficient access to data. [1] [2] [3] More precisely, a data structure is a collection of data values, the relationships among them, and the functions or operations that can be applied to the data, [4] i.e., it is an algebraic structure about data.
A linear operator : between two topological vector spaces (TVSs) is called a bounded linear operator or just bounded if whenever is bounded in then () is bounded in . A subset of a TVS is called bounded (or more precisely, von Neumann bounded ) if every neighborhood of the origin absorbs it.
Systolic arrays (< wavefront processors), first described by H. T. Kung and Charles E. Leiserson are an example of MISD architecture. In a typical systolic array, parallel input data flows through a network of hard-wired processor nodes, resembling the human brain which combine, process, merge or sort the input data into a derived result.
A reduct can be thought of as a sufficient set of features – sufficient, that is, to represent the category structure. In the example table above, attribute set {,,} is a reduct – the information system projected on just these attributes possesses the same equivalence class structure as that expressed by the full attribute set:
[0, 1] 2 is a totally bounded space because for every ε > 0, the unit square can be covered by finitely many open discs of radius ε. A metric space (,) is totally bounded if and only if for every real number >, there exists a finite collection of open balls of radius whose centers lie in M and whose union contains M.