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  2. List of types of functions - Wikipedia

    en.wikipedia.org/wiki/List_of_types_of_functions

    Continuous function: in which preimages of open sets are open. Nowhere continuous function: is not continuous at any point of its domain; for example, the Dirichlet function. Homeomorphism: is a bijective function that is also continuous, and whose inverse is continuous. Open function: maps open sets to open sets.

  3. Continuous function - Wikipedia

    en.wikipedia.org/wiki/Continuous_function

    the sinc-function becomes a continuous function on all real numbers. The term removable singularity is used in such cases when (re)defining values of a function to coincide with the appropriate limits make a function continuous at specific points. A more involved construction of continuous functions is the function composition.

  4. Scott continuity - Wikipedia

    en.wikipedia.org/wiki/Scott_continuity

    A Scott-continuous function is always monotonic, meaning that if for ,, then () (). A subset of a directed complete partial order is closed with respect to the Scott topology induced by the partial order if and only if it is a lower set and closed under suprema of directed subsets.

  5. List of mathematical functions - Wikipedia

    en.wikipedia.org/wiki/List_of_mathematical_functions

    Thomae's function: is a function that is continuous at all irrational numbers and discontinuous at all rational numbers. It is also a modification of Dirichlet function and sometimes called Riemann function. Kronecker delta function: is a function of two variables, usually integers, which is 1 if they are equal, and 0 otherwise.

  6. Extreme value theorem - Wikipedia

    en.wikipedia.org/wiki/Extreme_value_theorem

    A continuous function () on the closed interval [,] showing the absolute max (red) and the absolute min (blue). In calculus , the extreme value theorem states that if a real-valued function f {\displaystyle f} is continuous on the closed and bounded interval [ a , b ] {\displaystyle [a,b]} , then f {\displaystyle f} must attain a maximum and a ...

  7. Uniform continuity - Wikipedia

    en.wikipedia.org/wiki/Uniform_continuity

    Linear functions + are the simplest examples of uniformly continuous functions. Any continuous function on the interval [ 0 , 1 ] {\displaystyle [0,1]} is also uniformly continuous, since [ 0 , 1 ] {\displaystyle [0,1]} is a compact set.

  8. Fantasy Football Waiver Wire: Early pickups for Week 9 - AOL

    www.aol.com/sports/fantasy-football-waiver-wire...

    Bye weeks return in Week 9, so make sure you get those fantasy football lineups ready for action!

  9. Intermediate value theorem - Wikipedia

    en.wikipedia.org/wiki/Intermediate_value_theorem

    Intermediate value theorem: Let be a continuous function defined on [,] and let be a number with () < < ().Then there exists some between and such that () =.. In mathematical analysis, the intermediate value theorem states that if is a continuous function whose domain contains the interval [a, b], then it takes on any given value between () and () at some point within the interval.

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