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  2. Bounded operator - Wikipedia

    en.wikipedia.org/wiki/Bounded_operator

    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.

  3. Range query (computer science) - Wikipedia

    en.wikipedia.org/wiki/Range_query_(computer_science)

    Andrew Yao showed [3] that there exists an efficient solution for range queries that involve semigroup operators. He proved that for any constant c, a pre-processing of time and space () allows to answer range queries on lists where f is a semigroup operator in (()) time, where is a certain functional inverse of the Ackermann function.

  4. Operators in C and C++ - Wikipedia

    en.wikipedia.org/wiki/Operators_in_C_and_C++

    All the operators (except typeof) listed exist in C++; the column "Included in C", states whether an operator is also present in C. Note that C does not support operator overloading. When not overloaded, for the operators && , || , and , (the comma operator ), there is a sequence point after the evaluation of the first operand.

  5. Bounded function - Wikipedia

    en.wikipedia.org/wiki/Bounded_function

    A bounded operator: is not a bounded function in the sense of this page's definition (unless =), but has the weaker property of preserving boundedness; bounded sets are mapped to bounded sets (). This definition can be extended to any function f : X → Y {\displaystyle f:X\rightarrow Y} if X {\displaystyle X} and Y {\displaystyle Y} allow for ...

  6. Free variables and bound variables - Wikipedia

    en.wikipedia.org/wiki/Free_variables_and_bound...

    An instance of a variable symbol is bound, in contrast, if the value of that variable symbol has been bound to a specific value or range of values in the domain of discourse or universe. This may be achieved through the use of logical quantifiers, variable-binding operators, or an explicit statement of allowed values for the variable (such as ...

  7. Compact operator - Wikipedia

    en.wikipedia.org/wiki/Compact_operator

    Any compact operator is strictly singular, but not vice versa. [6] A bounded linear operator between Banach spaces is compact if and only if its adjoint is compact (Schauder's theorem). [7] If : is bounded and compact, then: [5] [7] the closure of the range of is separable.

  8. Open mapping theorem (functional analysis) - Wikipedia

    en.wikipedia.org/wiki/Open_mapping_theorem...

    The closed range theorem, which says an operator (under some assumption) has closed image if and only if its transpose has closed image (see closed range theorem#Sketch of proof). The open mapping theorem does not imply that a continuous surjective linear operator admits a continuous linear section. What we have is: [9]

  9. Bounds checking - Wikipedia

    en.wikipedia.org/wiki/Bounds_checking

    In computer programming, bounds checking is any method of detecting whether a variable is within some bounds before it is used. It is usually used to ensure that a number fits into a given type (range checking), or that a variable being used as an array index is within the bounds of the array (index checking).